U.S. patent number 6,882,477 [Application Number 09/711,019] was granted by the patent office on 2005-04-19 for method and system for interference lithography utilizing phase-locked scanning beams.
This patent grant is currently assigned to Massachusetts Institute of Technology. Invention is credited to Patrick N. Everett, Mark Schattenburg.
United States Patent |
6,882,477 |
Schattenburg , et
al. |
April 19, 2005 |
Method and system for interference lithography utilizing
phase-locked scanning beams
Abstract
A method and system of interference lithography (also known as
interferometric lithography or holographic lithography) which
utilizes phase-locked, scanning beams (so-called scanning beam
interference lithography, or SBIL). The invention utilizes a
high-precision stage that moves a substrate under overlapped and
interfering pairs of coherent beams. The overlapped beams
interfere, generating fringes, which form a pattern "brush" for
subsequent writing of periodic and quasi-periodic patterns on the
substrate. The phase of the fringes in the overlapped region is
phase-locked to the motion of the precision stage. The invention
includes methods for forming, overlapping, and phase-locking
interfering pairs of beams on a variety of substrates; methods for
measuring and controlling the period, phase, and angular
orientation of fringes generated by the overlapping beams; and
methods for measuring and controlling the effects of stage
mechanical and thermal drift and other disturbances during the
writing process.
Inventors: |
Schattenburg; Mark (Wayland,
MA), Everett; Patrick N. (Concord, MA) |
Assignee: |
Massachusetts Institute of
Technology (Cambridge, MA)
|
Family
ID: |
34437153 |
Appl.
No.: |
09/711,019 |
Filed: |
November 9, 2000 |
Current U.S.
Class: |
359/577;
359/35 |
Current CPC
Class: |
G03F
7/70383 (20130101); G03F 7/70408 (20130101); G03H
1/0486 (20130101); G03H 2001/0482 (20130101); G03H
2222/36 (20130101); G03H 2225/21 (20130101) |
Current International
Class: |
G03F
7/20 (20060101); G02B 027/00 () |
Field of
Search: |
;359/35,577,1,34,10,28 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
M L. Schattenburg, C. Chen, P. N. Everett, J. Ferrera, P. Konkola,
H. I. Smith, "Sub-100 nm Metrology using Interferometrically
Produced Fiducials", J. Vac. Sci. Tech. B, vol. 17, No. 6, pp.
2692-2697, 1999.* .
Schattenburg, M.L. et al., "Sub-100 nm metrology using
interferometrically produced fiducials," 43.sup.rd International
Conference on Electron, Ion, and Photon Beam Technology and
Nanofabrication, Marco Island, Fl., USA, Jun. 1-4, 1999, vol. 17,
No. 6, pp. 2692-2697. XP000955448 Journal of Vacuum Science &
Technology B (Microelectronics and Nanometer Structures), Nov.
1999, AIP for American Vacuum Soc, USA, ISSN: 0734-211X, p. 2696.
.
Patent Abstracts of Japan, vol. 14, No. 524 (E-1003), Nov. 16,
1990-&JP 02 220489 A (Mitsubishi Electric Corp), Sep. 3, 1990.
.
"Large-Area Achromatic Interferometric Lithography for 100 nm
Period Gratings and Grids," Savas et al. J. Vac. Sci. Technol.,
Nov./Dec. 1995. vol. 14..
|
Primary Examiner: Nguyen; Thong
Assistant Examiner: Lavarias; Arnel C.
Attorney, Agent or Firm: Gauthier & Connors LLP
Government Interests
GOVERNMENT SPONSORSHIP INFORMATION
The government has rights to this invention pursuant to contract
number NAG5-5105 awarded by the National Aeronautics and Space
Administration, and contract number DAAG55 -98-1-0130 awarded by
the Defense Advanced Projects Research Administration.
Parent Case Text
PRIORITY INFORMATION
This application claims priority from provisional application Ser.
No. 60/164,655 filed Nov. 10, 1999.
Claims
What is claimed is:
1. A method of writing patterns onto workpieces, comprising:
directing a plurality of beams to converge and substantially
overlap in a common region on a workpiece, each beam being mutually
coherent with at least one other of said beams such that, in the
region of overlap, overlapping beams form interference fringes to
define a writing image; relatively moving, while writing patterns
onto said workpiece, said workpiece with respect to said writing
image; measuring the phase of said interference fringes of said
writing image with respect to points on said workpiece; and
controlling, while writing patterns onto said workpiece and using
the measured phase of said interference fringes of said writing
image, the phases of said beams to correct for phase errors of said
interference fringes of said writing image.
2. The method according to claim 1 further comprising controlling,
while writing patterns onto said workpiece, positions, periods
and/or angles of said interference fringes.
3. The method according to claim 2, wherein said controlling the
positions, periods and/or angles of said interference fringes
comprises sensing, while writing patterns onto said workpiece,
positions, phases, periods and/or angles of said interference
fringes in order to provide feedback for correcting the positions,
phases, periods and/or angles of said interference fringes.
4. The method according to claim 2, wherein said controlling the
positions, periods and/or angles of said interference fringes
comprises controlling angles of said beams.
5. The method according to claim 4, wherein said controlling the
positions, periods and/or angles of said interference fringes
comprises sensing angles and/or phases of said beams in order to
provide feedback for correcting the positions, periods and/or
angles of said interference fringes.
6. The method of claim 2, wherein said controlling the positions,
periods and/or angles of said interference fringes comprises
sensing, while writing patterns onto said workpiece, relative
position and/or rotation of said workpiece in order to provide
feedback for correcting the positions, periods and/or angles of
said interference fringes.
7. The method according to claim 1, wherein said relatively moving
said workpiece with respect to said writing image comprises moving
said workpiece.
8. The method according to claim 1, wherein said relatively moving
said workpiece with respect to said writing image comprises moving
said writing image.
9. The method according to claim 1, wherein said relatively moving
said workpiece with respect to said writing image comprises moving
said interference fringes.
10. The method according to claim 1, further comprising controlling
the relative position and/or rotation of said interference fringes
with respect to said workpiece.
11. The method according to claim 10, wherein said controlling said
interference fringes comprises sensing a relative position and/or
rotation of said workpiece in order to provide feedback for
correcting the positions, periods and/or angles of said
interference fringes.
12. The method according to claim 10, wherein said controlling said
interference fringes comprises sensing the positions, phases,
periods and/or angles of said interference fringes in order to
provide feedback for correcting the positions, phases, periods
and/or angles of said interference fringes.
13. The method according to claim 10, wherein said controlling said
interference fringes comprises sensing angles and/or phases of said
beams in order to provide feedback for correcting the positions,
phases, periods and/or angles of said interference fringes.
14. The method according to claim 1 further comprising controlling
amplitudes and contrasts of said interference fringes.
15. The method according to claim 14, wherein said controlling
amplitudes and contrasts of said interference fringes comprises
sensing the amplitudes and contrasts of said interference fringes
in order to provide feedback for correcting the amplitudes and
contrasts of said interference fringes.
16. The method according to claim 14, wherein said controlling the
amplitudes and contrasts of said interference fringes comprises
controlling the intensities of said beams.
17. The method according to claim 16, wherein said controlling the
intensities of said beams comprises sensing the intensities of said
beams in order to provide feedback for correcting the intensities
of said beams.
18. The method according to claim 1, wherein said relatively moving
said workpiece with respect to said writing image comprises moving
with respect to relative translation, rotation and/or tilt.
19. The method according to claim 1, further comprising controlling
the relative position and/or rotation of said interference fringes
with respect to said workpiece such that said interference fringes
are substantially stationary in the reference frame of said
workpiece.
20. The method according to claim 1, further comprising
controlling, prior to writing patterns onto said workpiece,
positions, periods and/or angles of said interference fringes.
21. The method according to claim 20, wherein said controlling the
positions, periods and/or angles of said interference fringes
comprises sensing, prior to writing patterns onto said workpiece,
positions, phases, periods and/or angles of said interference
fringes in order to provide feedback for correcting the positions,
periods and/or angles of said interference fringes.
22. The method according to claim 20, wherein said controlling the
positions, periods and/or angles of said interference fringes
comprises controlling angles of said beams.
23. The method according to claim 22, wherein said controlling the
positions, periods and/or angles of said interference fringes
comprises sensing angles and/or phases of said beams in order to
provide feedback for correcting the positions, periods and/or
angles of said interference fringes.
24. The method of claim 20, wherein said controlling the positions,
periods and/or angles of said interference fringes comprises
sensing, while writing patterns onto said workpiece, relative
position and/or rotation of said workpiece in order to provide
feedback for correcting the positions, periods and/or angles of
said interference fringes.
25. A system for writing patterns onto workpieces, comprising:
means for directing a plurality of beams to converge and
substantially overlap in a common region on a workpiece, each beam
being mutually coherent with at least one other of said beams such
that, in the region of overlap, overlapping beams form interference
fringes to define a writing image; means for relatively moving,
while writing patterns onto said workpiece, said workpiece with
respect to said writing image; means for measuring the phase of
said interference fringes of said writing image with respect to
points on said workpiece; and means for controlling, while writing
patterns onto said workpiece and using the measured phase of said
interference fringes of said writing image, the phases of said
beams to correct for phase errors of said interference fringes of
said writing image.
26. The system according to claim 25, further comprising means for
controlling the relative position and/or rotation of said
interference fringes with respect to said workpiece.
27. The system according to claim 25, further comprising means for
controlling the relative position and/or rotation of said
interference fringes with respect to said workpiece such that said
interference fringes are substantially stationary in the reference
frame of said workpiece.
28. The system according to claim 25, further comprising means for
controlling, while writing patterns onto said workpiece, positions,
periods and/or angles of said interference fringes.
29. The system according to claim 25, further comprising means for
controlling, prior to writing patterns onto said workpiece,
positions, periods and/or angles of said interference fringes.
30. The system according to claim 28, wherein said means for
controlling the positions, periods and/or angles of said
interference fringes comprises means for sensing, while writing
patterns onto said workpiece, positions, phases, periods and/or
angles of said interference fringes in order to provide feedback
for correcting the positions, periods and/or angles of said
interference fringes.
31. The system according to claim 28, wherein said means for
controlling the positions, periods and/or angles of said
interference fringes comprises means for sensing, prior to writing
patterns onto said workpiece, positions, phases, periods and/or
angles of said interference fringes in order to provide feedback
for correcting the positions, periods and/or angles of said
interference fringes.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to interference lithography (IL), also known
as interferometric lithography or holographic lithography, a method
wherein periodic or quasi-periodic patterns are exposed into a
photosensitive material (in thin-film form, usually called a
resist), by overlapping pairs of phase-locked beams from a laser or
other intense source of radiation. In general, a beam, such as
emitted from a laser, is split into pairs of beams, which are then
directed to recombine at a resist-coated substrate. At the
intersection of the beams a periodic interference pattern is
created with period p=.lambda./(2 sin .theta.), where .lambda. is
the beam wavelength and .theta. is intersection half-angle of a
particular beam pair.
2. Description of Prior Art
A controlled phase relationship must hold between the two halves of
a beam pair, and between all sets of beam pairs (i.e., they must be
"phase-locked") in order to form stable, high-contrast fringes.
This can be achieved passively, by the use of a rigid, compact
optical system designed for thermal and mechanical stability, or
alternatively by the use of active optical components and
phase-error measuring sensors in conjunction with phase-locking
feedback electronics (see E. H. Anderson, H. I. Smith, and M. L.
Schattenburg, "Holographic Lithography," U.S. Pat. No.
5,142,385).
When a coherent source of light is used, such as a laser, the beam
is typically split with a dielectric beamsplitter and recombined
with mirrors (see H. I. Smith, "Fabrication techniques for surface
acoustic wave and thin-film optical devices," Proc. IEEE 62,
1361-1387 [1974]). In an alternative configuration, known as
achromatic interference lithography (AIL), the beam is split and
recombined using diffraction gratings (see T. A. Savas, M. L.
Schattenburg, J. M. Carter, and H. I. Smith, "Large-area achromatic
interferometric lithography for 100 nm period gratings and grids,"
J. Vac. Sci. Technol. B 14, 4167-4170 [1996]). In this second case,
beams lacking high spatial and temporal coherence can still be used
to make useful gratings. The AIL method utilizes much more compact
optics that the IL method, resulting in a very stable
interferometer. However, a disadvantage is that each AIL system can
pattern only a single period.
IL has been used commercially for many years to produce large-area
diffraction gratings for spectroscopy. Other industrial and
research applications for IL-patterned gratings and grids include:
optical components for filtering, polarizing, diffracting and other
manipulations of light, x-rays, and particle beams; length-scale
standards for metrology; positional encoders in motion control
equipment; fiducial grids used during spatial-phase locked
electron-beam lithography (see H. I. Smith, E. H. Anderson, and M.
L. Schattenburg "Energy beam locating," U.S. Pat. No. 5,136,169);
arrays of field emitter tips for flat panel display manufacturing
(see C. O. Bozler et al., "Arrays of gated field-emitter cones
having a 0.32 .mu.m tip-to-tip spacing," J. Vac. Sci. Technol. B
12, 629 (1994)); and high density magnetic storage (see M. Farhoud
et al., "Fabrication of large area nanostructured magnets by
interferometric lithography," IEEE Trans. Mag. 34, 1087-1089
(1998)).
Competitive non-IL means of producing precision periodic
patterns'suffer from a number of well-known deficiencies. For
example, the technique of mechanical ruling suffers from extremely
slow speed, poorly-controlled grating groove profile, inability to
pattern very fine periods, distortions due to limited servo-loop
gain, and incompatibility with semiconductor lithographic
processing. The method of energy beam writing (e.g., electron, beam
lithography or ion beam lithography) suffers from slow speed and
large grating distortions due to poor beam positioning control
(e.g., stitching errors).
In general, IL methods are presently superior to competing methods
for rapidly producing precision periodic patterns. In current IL
practice, large-area patterns are generally achieved by expanding
the beams with lenses, after which they are caused to overlap and
interfere. Beams with spherical wavefronts can be achieved by using
a short-focal-length lens followed by an (optional) spatial-filter
pinhole at the lens focus. However, the interference of spherical
beams produces gratings with large hyperbolic distortions. Gratings
substantially free of hyperbolic distortions can be achieved by
following the spatial filter with a second, collimating lens.
However, in this case, distortions in the collimating lens due to
inevitable manufacturing errors are directly translated into
distortions in the grating. In addition, the collimating lens must
be at least as large as the substrate being patterned. Thus, for
good results, an IL system with large, precisely figured optics
and/or very long optical paths is required. Such a system is bulky,
expensive, and vulnerable to the distorting effects of vibration,
air turbulence, and thermal fluctuations. Uniform exposure dose is
also difficult to achieve. It is also difficult, expensive, and
time consuming to reconfigure such a system in order to fabricate
other types of general periodic patterns such as gratings with
other periods, grids (crossed gratings), and "chirped" gratings
with variable periods.
The AIL method, on the other hand, avoids the need for a highly
coherent source and is also more stable than the traditional IL
method due to its compact design, but does require splitter and
recombiner grating optics of superb quality which are at least as
large as the desired substrate size. In addition, the AIL method is
even less flexible that the IL method for patterning general
periodic patterns, since each AIL interferometer is designed to
pattern only one period.
Thus, current practice does not allow the rapid and low-cost
patterning of large, low distortion, general periodic and
quasi-periodic patterns with highly uniform and controlled
properties. The object of this invention is to provide these
benefits by utilizing novel means of conducting IL with
phase-locked scanning beams.
SUMMARY OF THE INVENTION
The invention provides a lithographic method and system of scanning
beam interference lithography (SBIL). In the most general
embodiment, this method and system utilizes matched pairs of
coherent, phase-locked, overlapped writing beams incident on a
substrate, which is coated with a photo-definable layer such as a
lithographic resist. Alternatively, substrates incorporating
regions of photosensitive material, such as sheets of lithium
niobate, or optical fibers with SiGe oxide cores, may be used. The
writing beam pairs are generated such that a carefully-controlled
phase relationship exists between left and right beam pair halves,
and between all beam pairs, which results in coherent interference
and thus the generation of periodic patterns in the area of overlap
(the "image"). The writing beams are typically much smaller in
diameter than the substrate. Any number of overlapping beam pairs
may be used, wherein the overlap region of all beam pairs on the
substrate coincide. The substrate is chucked to a commercial,
high-precision, three-axis (x-motion, y-motion, .gamma.-rotation)
motion stage, which is controlled by servo motors, a stage-position
sensor such as a laser interferometer or optical encoder, a
substrate surface z-height sensor, and control electronics. As the
substrate is scanned by the x-y stage, the angles, phases, and
amplitudes of the writing beams are controlled in a prescribed way
to inscribe useful precision periodic patterns on the
substrate.
Numerous other features and advantages of the invention will become
apparent from the following descriptions when read in connection
with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic block diagram of an exemplary embodiment of a
SBIL system in accordance with the invention including a
high-precision three-axis stage (two planar and one rotational
degrees of freedom) whose position is sensed by a three-axis
optical encoder, a writing interferometer that forms fringes on the
substrate, and rigid support blocks that accurately registers stage
and writing interferometer;
FIG. 2a is a schematic block diagram of an alternative embodiment
of a SBIL system that measures stage position with a two-axis laser
interferometer and a rotational optical encoder;
FIG. 2b is a schematic block diagram of another alternative
embodiment of a SBIL system that utilizes a two-axis laser
interferometer and a rotational optical encoder to measure stage
position with respect to the writing interferometer, and a third
interferometer axis to measure substrate height;
FIG. 3 is a diagram showing the detail of the overlap region of
coherent beams, resulting in a periodic interference-fringe "image"
which is exposed into a photosensitive resist layer on the
substrate;
FIG. 4a is a graph showing the irradiance distribution resulting
from left beam alone impinging on substrate;
FIG. 4b is a graph showing the irradiance distribution resulting
from right beam alone impinging on substrate;
FIG. 4c is a graph showing the irradiance distribution resulting
from overlap and interference of left and right beams on substrate,
resulting in an interference-fringe image;
FIG. 5a shows a scanning method that moves the substrate under a
small grating image in a boustrophedonic manner, where the
direction of motion is parallel to the fringe direction, thus
filling a much larger region of the substrate with grating
pattern;
FIG. 5b shows the grating image, as it would appear on a stationary
substrate;
FIG. 6 is a graph that depicts a method for overlapping successive
scans such that a uniform dose is achieved;
FIG. 7a shows the effect of stage-path lateral error on travel
straightness during grating scanning;
FIG. 7b shows the effect of stage path lateral error on the phase
of written grating;
FIG. 7c shows the effect of stage path yaw error on the contrast of
written grating;
FIG. 8a is a diagram presenting nomenclature of phase and frequency
during overlap of interfering beams;
FIG. 8b is a graph presenting nomenclature of fringe period,
position, and velocity;
FIG. 8c is a schematic block diagram of an exemplary embodiment of
the invention using a method for control of image phase utilizing
an actuator-controlled mirror;
FIG. 9 shows an alternative scanning method to that depicted in
FIG. 5a utilizing Doppler-shifted beams to scan the substrate in a
boustrophedonic manner, where the direction of motion is
perpendicular to the fringe direction;
FIG. 10a is a diagram presenting nomenclature of phase, frequency,
and angle for multiple beams;
FIG. 10b is a schematic block diagram of an exemplary embodiment of
the invention using a method of forming four-beam scanning
interferometer;
FIG. 10c shows an image resulting from two beams;
FIG. 10d shows an image resulting from four beams in two,
perpendicular, planes of incidence;
FIG. 11a shows an image resulting from interfering one beam
pair;
FIG. 11b shows an image resulting from interfering two in-plane
beam pairs;
FIG. 11c shows an image resulting from interfering three in-plane
beam pairs;
FIG. 11d shows an image resulting from interfering two
perpendicular-plane beam pairs;
FIG. 12 is a diagram showing a method for writing gratings onto
optical fibers using Doppler scanning;
FIG. 13a is a diagram showing a method for writing rotational
grating patterns onto a disk substrate;
FIG. 13b is a diagram showing a method for writing radial grating
patterns onto a disk substrate using Doppler scanning;
FIG. 13c is a diagram showing a method for writing grid patterns
onto disk substrate using four simultaneous unshifted and
Doppler-shifted beams;
FIG. 14a is a schematic block diagram of an exemplary embodiment
showing a writing interferometer utilizing beam expander to control
image diameter;
FIG. 14b shows distortion in a grating image due to imperfections
in writing interferometer optics;
FIG. 14c shows reduced distortion in a grating image resulting from
reduced beam diameter;
FIG. 15a is a schematic diagram of an exemplary embodiment of a
writing interferometer utilizing pinhole spatial filters;
FIG. 15b is a schematic diagram of an exemplary embodiment of a
writing interferometer utilizing fiber optic spatial filters;
FIG. 15c shows hyperbolic distortion in a grating image due to
spherical beams from spatial filters;
FIG. 15d shows reduced grating image distortion resulting from
reduced beam diameter;
FIG. 16a is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing pinhole spatial filters and
collimating lenses;
FIG. 16b shows a resulting grating image with eliminated hyperbolic
distortion.
FIG. 17a is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing a transmission grating
beamsplitter and plus/minus first-order beam interference;
FIG. 17b is a diagram showing details of the writing
interferometer, showing first-order diffracted beams and grating
image in region of overlap;
FIG. 18a is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing a transmission grating
beamsplitter and zero/first-order beam interference;
FIG. 18b is a diagram showing details of the writing
interferometer, showing zero- and first-order diffracted beams and
grating image in region of overlap;
FIG. 19a is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing transmission gratings for beam
splitting and recombining;
FIG. 19b is a schematic block diagram of another exemplary
embodiment of a writing interferometer utilizing transmission
grating beamsplitter and lens beam recombiner;
FIG. 19c is a schematic block diagram of another exemplary
embodiment of a writing interferometer utilizing transmission
grating beamsplitter and objective lens recombiner, the objective
lens featuring a spatial filter plate at the Fourier plane of the
lens;
FIG. 19d is a top view of a spatial filter plate designed to allow
patterning of only one grating period;
FIG. 19e is a top view of a spatial filter plate designed to allow
patterning parallel gratings with a range of periods;
FIG. 19f is a top view of a spatial filter plate designed to allow
patterning of only two perpendicular grating periods;
FIG. 19g is a top view of a spatial filter plate designed to allow
patterning perpendicular gratings with a range of periods;
FIG. 20a shows a boustrophedonic scheme for patterning linear
variable-period gratings;
FIG. 20b shows a boustrophedonic scheme for patterning curved
variable-period gratings;
FIG. 21 is a schematic block diagram of an exemplary embodiment of
a writing interferometer for patterning variable-period
gratings;
FIG. 22a is a schematic block diagram of an exemplary embodiment of
a writing interferometer for patterning variable-period gratings
that utilizes an actuator-controlled mirror for selecting the
interferometer-arm 2.theta. angle, and thus the grating period, a
mirror beamsplitter for forming the opposing arm of the
interferometer, and an objective lens for projecting the grating
image onto the substrate;
FIG. 22b is a schematic block diagram of an alternative
2.theta.-angle selector utilizing an electro-optic beam
deflector;
FIG. 22c is a schematic block diagram of an alternative
2.theta.-angle selector utilizing an acousto-optic beam
deflector;
FIG. 22d is a schematic block diagram of an exemplary embodiment of
a mirror beamsplitter, which splits incident beams into parallel
and mirrored beams;
FIG. 23a is a schematic block diagram of an exemplary embodiment of
a writing interferometer employing individual electro-optic (EO)
beam deflectors for each arm to affect 2.theta.-angle selection,
where both EO deflectors are driven simultaneously by the same
controller, and the left and right deflected beams are superimposed
by a beamsplitter and imaged onto the substrate by an objective
lens;
FIG. 23b is a schematic block diagram of an exemplary embodiment of
a writing interferometer similar to that depicted in FIG. 23a, but
employing acousto-optic (AO) beam deflectors to affect beam angle
selection, the AO modulators are driven by the same control signal,
which constitutes an ensemble of RF frequencies, each modulator RF
driver frequency generates a distinct pair of beams on the
substrate, and thus a distinct spatial frequency component in the
image, enabling complex image patterning to be achieved;
FIG. 23c is a schematic block diagram of an exemplary embodiment of
a writing interferometer similar to that depicted in FIG. 23b, but
employing a grating to superimpose the left and right diffracted
beams;
FIG. 24a is a schematic block diagram of an exemplary embodiment of
a writing interferometer with similar functionality as that
depicted in FIG. 23b, but which employs a special dual crossed-beam
acoustic-beam modulator to achieve a more compact system, however,
bandwidth considerations limit the angular range between
.theta..sub.(min) <.theta.<.theta..sub.(max), as
depicted;
FIG. 24b is a schematic block diagram of an exemplary embodiment of
a writing interferometer similar to that depicted in FIG. 24a, but
which employs an angular subtraction optic to expand the available
range of angles;
FIG. 24c shows an exemplary prism-based angular subtraction
optic;
FIG. 24d shows an exemplary grating-based angular subtraction
optic;
FIG. 24e is a top-view of a two-crossed-beam acousto-optic
deflector;
FIG. 24f is a top-view of a four-crossed-beam acousto-optic
deflector;
FIG. 25 is a schematic block diagram of an exemplary embodiment of
a SBIL system utilizing a phase reference interferometer to measure
the phase error between the arms of the writing interferometer and
an actuated mirror for manipulating the phase of one of the
interferometer arms, thus enabling phase-locking of the grating
image to the moving substrate;
FIG. 26a is a graph demonstrating the limited phase range of
actuated mirror and electro-optic phase shifters;
FIG. 26b is a graph demonstrating the use of flyback to achieve
semi-continuous phase over phase ranges exceeding the capability of
a limited phase-shifting optic;
FIG. 26c is a graph demonstrating the use of flyback to achieve
sustained frequency shifts with a limited phase-shift optic;
FIG. 27a is a schematic block diagram of an exemplary embodiment of
a homodyne phase reference interferometer (PRI) of identical design
as depicted in FIG. 25;
FIG. 27b is a schematic block diagram of an exemplary embodiment of
a heterodyne PRI, in which Doppler-shifted light is delivered by
the optical fiber to the PRI and mixed individually with the left
and right interferometer arms, and signals representing heterodyne
versions of the left and right arms are subtracted electronically
to yield the writing interferometer phase difference;
FIG. 27c is a diagram showing a method employing an AO modulator
for splitting a weak Doppler-shifted heterodyne beam from the main
writing interferometer beam, the heterodyne beam is inserted into
an optical fiber for delivery to the heterodyne PRI, while the main
beam proceeds to the writing interferometer;
FIG. 28 is a schematic block diagram of an exemplary embodiment of
a heterodyne PRI using a method that avoids the use of a separate
heterodyne beam by employing an in-line AO modulator and
birefringent crystal;
FIG. 29a is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing a homodyne phase-reference
interferometer with a mirror beamsplitter to interfere left and
right writing interferometer arms with each other on an imaging
detector;
FIG. 29b is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing a homodyne phase-reference
interferometer that forms a magnified image on an imaging
detector;
FIG. 30 is a schematic block diagram of an exemplary embodiment of
a writing interferometer utilizing a heterodyne phase-reference
interferometer that uses a mirror beamsplitter to interfere
variable-period heterodyne beams with split writing interferometer
beams on an imaging detector;
FIG. 31 is a schematic block diagram of an exemplary embodiment of
a writing interferometer configured with a combination of
actuator-controlled mirror and electro-optic (EO) phase
shifters;
FIG. 32 is a schematic block diagram of an exemplary embodiment of
a writing interferometer configured with grating beamsplitter
pushed by mechanical actuator for the purpose of controlling image
phase;
FIG. 33a is a schematic block diagram of an exemplary embodiment of
a writing interferometer configured with a spinning grating disk
and actuator-controlled mirror for the purpose of controlling image
phase;
FIG. 33b is a plan view of a spinning grating disk;
FIG. 34 is a schematic block diagram of an exemplary embodiment of
a writing interferometer configured with acousto-optic (AO)
frequency modulators in each arm for the purpose of controlling the
image phase and frequency;
FIG. 35 is a schematic block diagram of an exemplary embodiment of
a writing interferometer configured with acousto-optic (AO)
frequency modulators and electro-optic (EO) beam deflectors in each
arm, the AO modulators control image phase, while the EO deflectors
remove the undesired beam deflections that are associated with
frequency modulation;
FIG. 36 is a schematic block diagram of an exemplary embodiment of
a writing interferometer employing EO deflectors to control image
period and AO deflectors to control image phase and frequency;
FIG. 37a shows the effect of dynamic image phase error on a grating
stripe during substrate scanning;
FIG. 37b shows the effect of dynamic image period error on a
grating stripe during substrate scanning;
FIG. 37c shows the effect of dynamic image rotation error on a
grating stripe during substrate scanning;
FIG. 38a is a schematic diagram showing a method for measurement of
writing arm angles and deflections during writing;
FIG. 38b is a schematic diagram showing an alternative method for
measurement of writing arm angles and deflections during
writing;
FIG. 39 is a schematic diagram showing a homodyne method for
measurement of writing arm angles, deflections, and phase
difference during writing;
FIG. 40 is a schematic diagram showing a heterodyne method for
measurement of writing arm angles, deflections, and phase
difference during writing;
FIG. 41a is a schematic diagram showing a method employing
actuator-controlled mirrors for manipulating writing arm angles and
deflections during writing;
FIG. 41b is a schematic diagram showing a method employing
electro-optic beam deflectors for manipulating writing arm angles
and deflections during SBIL writing;
FIG. 42a is a schematic block diagram of an exemplary embodiment of
a SBIL system configured as a writing interferometer (not showing
phase-reference interferometer and optics for manipulating
writing-arm angle, deflection, and phase), demonstrating the
location of components on substrate stage for the purpose of
measuring image period, angle, and phase, used when configured as a
reading interferometer;
FIG. 42b is a schematic block diagram of an exemplary embodiment of
a SBIL system, as it would appear when stage has been moved such
that beams impinge on position-sensitive detector for the purpose
of beam centering and overlapping;
FIG. 42c is a schematic block diagram of an exemplary embodiment of
a SBIL system configured as a reading interferometer, the stage has
been moved such that beams impinge on phase-sensing beamsplitter
and detector(s), for the purpose of measuring image period,
rotation, and phase;
FIG. 42d is a schematic block diagram of an exemplary embodiment of
a SBIL system configured as a reading interferometer, the stage has
been moved such that beams impinge on phase-sensing grating and
detector(s), for the purpose of measuring image rotation and
phase;
FIG. 43a is a schematic block diagram of an exemplary embodiment of
a SBIL system similar to as depicted in FIG. 25, configured in
writing-interferometer mode, showing detail of substrate stage and
phase-reference interferometer, reading-interferometer optics are
idle in this mode;
FIG. 43b is a schematic block diagram showing the same system as
FIG. 43a configured in reading-interferometer mode, showing detail
of substrate stage and phase-reference interferometer, image phase
detection is performed using a homodyne scheme;
FIG. 43c is a schematic block diagram showing the same system as
FIG. 43a configured in reading-interferometer mode, showing detail
of substrate stage and phase-reference interferometer, image phase
detection is performed using an in-line heterodyne scheme, where a
writing-interferometer configuration such as depicted in FIG. 34 is
used to provide Doppler shifting of the writing arms;
FIG. 44a is a schematic block diagram of an exemplary embodiment of
a SBIL system similar to as depicted in FIG. 27a and 27b,
configured in writing-interferometer mode, showing detail of
substrate stage and heterodyne phase-reference interferometer,
reading-interferometer optics are idle in this mode;
FIG. 44b is a schematic block diagram showing the same system as
FIG. 44a configured in reading-interferometer mode, image phase
detection is performed using an in-line heterodyne scheme, where a
writing-interferometer configuration such as depicted in FIG. 34 is
used to provide Doppler shifting of the writing arms;
FIG. 45a is a schematic block diagram of an exemplary embodiment of
a SBIL system in writing mode, showing heterodyne phase-reference
interferometer identical as depicted in FIG. 27b and 27c, and
components of an idle heterodyne reading-interferometer attached to
the stage;
FIG. 45b is a schematic block diagram showing the same system as
FIG. 45a in reading mode, where image phase is read using a
heterodyne scheme;
FIG. 46a is a schematic diagram of an exemplary embodiment of a
reading interferometer using beamsplitter cube and detectors to
measure phase between left and right beams;
FIG. 46b is a schematic diagram of an exemplary embodiment of a
reading interferometer using redirecting mirrors, beamsplitter
cube, and detectors to measure phase between left and right
beams;
FIG. 46c is a schematic diagram of an exemplary embodiment of a
reading interferometer using objective lens, beamsplitter cube, and
detectors to measure phase between left and right beams;
FIG. 46d is a schematic diagram of an exemplary embodiment of a
reading interferometer that utilizes detector to measure phase
between left and right beams;
FIG. 46e is a schematic diagram of an exemplary embodiment of a
reading interferometer using lens and detector to measure phase
between left and right beams;
FIG. 46f is a schematic diagram of an exemplary embodiment of a
reading interferometer using pinhole and detector to measure phase
between left and right beams;
FIG. 46g is a schematic diagram of an exemplary embodiment of a
reading interferometer using pinhole, optical fiber, and detector
to measure phase between left and right beams;
FIG. 46h is a schematic diagram of an exemplary embodiment of a
reading interferometer using scatterer and detector to measure
phase between left and right beams;
FIG. 47a shows a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage prism mirror, image phase is
measured by interfering beams from each arm with beams from the
same arm reflected from the prism;
FIG. 47b is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage prism mirror, image phase is
measured by interfering beams from each arm with beams from the
same arm reflected from the prism, in the special case that the
incident and reflected beams from the prism are coincident;
FIG. 47c is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage prism mirror, image phase is
measured by interfering beams from each arm reflected from prism
with beams from the opposite arm reflected from prism;
FIG. 47d is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage prism mirror, image phase is
measured by interfering beams from each arm reflected from prism
with beams from the opposite arm reflected from prism, in the
special case that the incident and reflected beams from the prism
are coincident;
FIG. 48a is a schematic diagram of an exemplary embodiment of a
heterodyne reading interferometer utilizing stage prism mirror,
image phase is measured by interfering beams from each arm
reflected from prism with heterodyne beams;
FIG. 48b is a schematic diagram of an exemplary embodiment of a
heterodyne reading interferometer utilizing stage prism mirror,
image phase is measured by interfering beams from each arm
reflected from prism with heterodyne beams, in the special case
that the incident and reflected beams from the prism are
coincident;
FIG. 49a is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beam from each arm diffracted by
the gratings with beams from the same arm reflected from the
grating;
FIG. 49b is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with beams from the opposite arm;
FIG. 49c is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with beams from the opposite arm diffracted by the
grating;
FIG. 49d is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with beams from the opposite arm diffracted by the
grating, where the diffracted beamns are coincident;
FIG. 49e is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with beams from the same arm;
FIG. 49f is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with beams from the opposite arm reflected by the
grating;
FIG. 49g is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with light from the opposite arm reflected by the
grating, where the incident, diffracted, and reflected beams are
coincident;
FIG. 49h is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing stage reflection grating, image
phase is measured by interfering beams from each arm diffracted by
the grating with beams from the opposite arm reflected by the
grating, where the diffracted and reflected beams are coincident,
and cast into a different plane than the incident beams by tilting
the plane of incidence;
FIG. 50 is a schematic diagram of an exemplary embodiment of a
heterodyne reading interferometer utilizing a stage reflection
grating, interfering beams diffracted from each arm with heterodyne
beams measure image phase;
FIG. 51a is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing a stage transmission grating,
image phase is measured by interfering beams from each arm
transmitted by the grating with beams from the opposite arm
diffracted from the grating, such that the zero order of each arm
is coincident with a diffracted order of the opposite arm;
FIG. 51b is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing a stage transmission grating,
image phase is measured by interfering beams from each arm
diffracted by the grating with beams from the opposite arm
diffracted by the grating, such that diffracted beams are
coincident;
FIG. 51c is a schematic diagram of an exemplary embodiment of a
reading interferometer utilizing a stage transmission grating,
image phase is measured by interfering beams from each arm
diffracted by the grating with light from the opposite arm
diffracted by the grating, such that diffracted beams are not
coincident; and
FIG. 52 is a schematic diagram of an exemplary embodiment of a
heterodyne reading interferometer utilizing a stage transmission
grating, interfering beams diffracted from each arm with heterodyne
beams measure image phase.
DETAILED DESCRIPTION OF ILLUSTRATED EMBODIMENTS
With reference now to the drawings and more particularly. FIG. 1
thereof, there is shown a pictorial representation of a
scanning-beam interference lithography (SBIL) system in accordance
with the invention.
A laser 11, of wavelength .lambda. such as an argon-ion laser
operating at the UW wavelength of .lambda.=351 nm, emits a narrow
beam that strikes shutter/attenuator 12. Shutter/attenuator 12 can
be controlled electronically to commence the operation of SBIL by
directing a portion of the beam to the remainder of the apparatus,
comprising an interferometer. The interferometer, called the
writing interferometer, comprises a dielectric beamsplitter 14
which creates two beams, a variable attenuator 15 for adjusting the
irradiance of one of the beams until both match, and mirrors 16 for
redirecting the beams onto substrate 17. Alternatively, a cube
beamsplitter, or transmission or reflection grating beamsplitter,
may be substituted for dielectric beamsplitter 14. The split beams
are adjusted to overlap on the substrate, creating interference
fringes in the plane of the substrate of period p=.lambda./(2 sin
.theta.), where .theta. is half the angle between the arms of the
interferometer, also called the half angle or azimuthal angle. The
writing interferometer is mounted to rigid vertical optical bench
20, which in turn is mounted to rigid horizontal table 22 by rigid
vertical riser block 21. Table 22 supports a precision horizontal
(x-y) motion stage 30, which in turn supports precision rotary
stage 30b, to which is chucked substrate 17. Stage 30 provides
precision x-y motion, and rotary stage 30b provides optional
.gamma. rotation (yaw), of substrate 17, while fixing substrate
height z. Stages 30 may provide motion by the use of precision
actuators, such as servomotors, and smooth ways such as air,
magnetic, or roller bearings. An optical encoder comprising sensor
31, attached to stage 30, and grating 32, attached to table 22
detects stage x-position. Encoder sensor 31 generates time-varying
sinusoidal signals that are analyzed by stage position-sensor
controller 35 to determine the x-position of the stage. Similar
optical encoders provide y-axis, and optional substrate yaw,
positional information. High-precision optical encoders of
sophisticated design are commercially available. Stage
position-sensor controller 35 provides substrate x-position x.sub.S
(t), x-velocity u.sub.S (t)=dx.sub.S /dt, y-position y.sub.S (t),
y-velocity v.sub.S (t)=dy.sub.S /dt, yaw rotation angle
.gamma..sub.S (t), and spin .omega..sub.S (t)=d.gamma..sub.S /dt,
to servo-control electronics 1, which controls the stage position
to a prescribed location or path.
A higher-accuracy stage position sensing method is depicted in FIG.
2a. Laser 40, such as a helium-neon laser operating at the 632.8 nm
wavelength, is split by beamsplitter 41 to create two beams. The
vertical split beam is reflected by reference mirror 42 and
directed back through beamsplitter 41 to detector 44, while the
horizontal split beam is reflected by test mirror 43, which returns
beam to beamsplitter 41, which in turn directs the beam to detector
44. Test mirror 43 is attached to moving stage 30, while
beamsplitter 41 and reference mirror 42 are attached to rigid
reference block 23, which is in turn rigidly attached to table 22.
Interference of overlapped horizontal and vertical beams on
detector 44 generates time-varying sinusoidal signals that are
analyzed by stage position-sensor controller 35 to determine the
x-position and velocity of the sample. A similar interferometer
provides stage y-position and velocity information, while a rotary
encoder provides substrate yaw and spin information.
Displacement-measuring interferometers of sophisticated design,
with high precision and accuracy, are commercially available.
Servo-control electronics 1 uses information from the positional
interferometers to sense and control the stage position to a
prescribed location or path.
An improved stage interferometer design is depicted in FIG. 2b.
This design ameliorates problems associated with mechanical and
thermal disturbances in optical bench 20 and riser block 21, which
could generate undetected shifts of the fringes generated by the
writing interferometer. This design is similar to that depicted in
FIG. 2a, except that the vertical split beam from beamsplitter 41
is reflected by turning mirror 45 to reference mirror 42, which
reflects beam back to turning mirror 45 and then through
beamsplitter 41 to detector 44, where it interferes with the
horizontal split beam. Reference mirror 42 is rigidly mounted to
optical bench 20 near the center of the writing interferometer,
providing a much more accurate measurement of the substrate
position relative to the writing interferometer, thus significantly
reducing the effects of mechanical disturbances in optical bench 20
and riser block 21, such as vibration or thermal expansion.
Another feature of the interferometer design depicted in FIG. 2b is
a z-axis interferometer, which is useful to measure the z-position
z=z.sub.S (t) and z-velocity w.sub.S (t)=dz.sub.S /dt of the
surface of substrate 17 under the image. This will be of importance
in interferometer designs introduced hereinafter, where multiple
interfering beam pairs are used and image depth-of-focus is an
issue. This is due to the well-known fact that while the image
generated by the interference of a pair beams is independent of
z-height (i.e., gratings have "infinite depth of focus"), the image
generated by multiple coherently-interfering beam pairs (i) with
different azimuthal angles, .theta..sub.(i), changes with substrate
z-height, and has the desired character only within a narrow
z-range depth of focus. In this design an additional beamsplitter
120 splits a portion of the beam from laser 40 upward to the
z-interferometer, which is rigidly attached to optical bench 20.
Turning mirrors 121 and 122 direct beam to beamsplitter 130, which
splits beam into horizontal and vertical parts. Horizontal beam
reflects from reference mirror 131 back through beamsplitter 130 to
detector 132. Vertical beam reflects from substrate 17 back to
beamsplitter 130, which also directs it to detector 132.
Interference of overlapped horizontal and vertical beams on
detector 132 generates time-varying sinusoidal signals, which are
analyzed by stage position-sensor controller 35 to determine the
z-position and velocity of the substrate. Many other schemes for
substrate height sensing are in use and may be practical for
application in a SBIL system. Methods for using the z-height
information to eliminate the deleterious effects of being out of
focus are described hereinafter.
Substrate 17 is shown in more detail in FIG. 3. Substrate 17
incorporates a photosensitive layer 18, called a resist, which is
capable of recording fine-period patterns generated by the
interferometer. Writing interferometer left beam 25 and right beam
26, both incident in the x-z plane and with diameter d, overlap and
interfere in region 27 over substrate 17. In region 27 a grating
standing wave is formed, with period p given by p=.lambda./(2 sin
.theta.), comprising fringe planes filling the volume of
intersection 27, where the planes are parallel to the y-z axis with
plane spacing given by p. Interference region 27 is typically much
smaller in size than the substrate. For example, when using an
argon-ion laser with wavelength .lambda.=351.1 nm and a half-angle
.theta.=61.37 deg., a period p=200 nm is obtained. Typical diameter
of beams emitted from ion lasers are .about.1 mm, which is some
5000 times larger than the example grating period. The 1
mm-diameter beam is typically, in turn, some 10-1000 times smaller
than substrate sizes of interest.
The effect of interference of the overlapping left and right beams
on substrate 17 is shown in FIG. 4, wherein the irradiance
distribution in resist 18 on substrate 17, called the image, is
plotted vs. position x, for beams of diameter d incident in the x-z
plane. FIG. 4a depicts the irradiance distribution 36 in resist 18,
with diameter d.sub.par =d/cos .theta. in the direction parallel to
the plane of incidence, and d.sub.pep =d in the direction
perpendicular to the plane, obtained if only left beam 25 is
allowed to impinge on the substrate while right beam 26 is blocked.
A so-called Gaussian intensity distribution is depicted, which is
typical of optical systems illuminated by laser radiation. FIG. 4b
depicts the irradiance distribution 37 in resist 18 obtained if
only right beam 26 is allowed to impinge on the substrate, while
left beam 25 is blocked. FIG. 4c depicts the irradiance
distribution 38 in resist 18 resulting if both right beam 25 and
left beam 26 are allowed to simultaneously impinge and interfere,
resulting in a periodic interference pattern of period p.
FIG. 5a depicts a preferred method for "parallel scanning" small
grating image 38, with fringes parallel to the y-axis, over a large
substrate 17, resulting in a large grating 39. For clarity, FIG. 5b
depicts image 38, as it would appear on a stationary substrate.
Substrate 17 is chucked to precision motion stage 30. For clarity
rotary stage 30b is not depicted. The range of motion of stage 30
is typically larger than the size of substrate 17. Mirror 43a,
attached to stage 30, is used by the x-axis stage interferometer,
and mirror 43b, also attached to stage 30, is used by the y-axis
stage interferometer. The writing interferometer is carefully
adjusted so that the grating fringes in image 38 are parallel to
the y-axis. Stage 30 is first positioned such that grating image 38
is placed in the stage lower left-hand corner, beyond substrate 17.
Stage 30 is then moved smoothly in the -y direction, while being
held at a fixed x position, such that a long, narrow grating strip
is exposed into resist coating 18 on substrate 17. Stage 30 is
allowed to continue moving in they direction such that grating
image 38 moves off of substrate 17. Stage 30 is then stopped and
held at a fixed y position, and subsequently moved in the -x
direction by a distance .DELTA.x=Mp, such that
.DELTA.x<<d.sub.par is a modest fraction of the parallel
image diameter d.sub.par, say 10-50%, while simultaneously being an
exact integer multiple M of grating period p. Stage 30 is then
moved smoothly in the +y direction, while being held at fixed
x-.DELTA.x position, such that a second, long, narrow grating
strip, adjacent and in phase with the first scan, is exposed into
resist 18. Successive scans are then repeated, in a boustrophedonic
fashion, until the exposure of the desired region is completed. In
this way, if the interferometer is sufficiently stable, the
interferometer optics are of sufficient quality, and the x-y stage
motion is sufficiently smooth and accurate, then large-area
low-distortion gratings on substrate 17 are achieved. FIG. 6
demonstrates how a uniform exposure dose over a large area is
achieved by the described method of partially overlapping
sequential boustrophedonic scans of a Gaussian beam. Many other
writing schemes are possible other than the boustrophedonic scheme.
A description will be provided of the conditions that must hold
during arbitrary writing paths to avoid image smearing.
The parallel-scanning method requires a low-distortion grating
image, which would result from the use of high-quality optics in
the writing interferometer. A high-quality stage is also required
in order to avoid smearing the grating image during scanning. For
best results, the grating image should have distortion of less than
approximately 20% of the period, otherwise a large loss of contrast
in the final grating will occur. In addition, the
straightness-of-travel and yaw of the x-y stage during scanning
should also be very good, otherwise loss of contrast and large
grating distortions will occur. Stage path errors are common in
motion-control systems due to stage air bearing and reference
mirror flatness errors, vibration, thermal expansion, air
turbulence, and finite servo loop gain of the control electronics,
especially at higher scanning speeds. For best results, the stage
travel straightness and yaw should also contribute errors that are
less than approximately 20% of the period.
FIG. 7a defines some of the parameters of interest in the
discussion of stage path errors. In the figure, stage 30 has been
commanded to move from desired starting point 180 to ending point
181 along path 182 such that stage x-position x.sub.S =x.sub.0 and
yaw .gamma..sub.S =.gamma..sub.0 are constant with time t. However,
due to stage errors, the actual stage motion 183 occurs with
x-position x.sub.S (t) and yaw .gamma..sub.S (t). The error between
desired path 182 and actual path 183 results in stage position
error .delta.x.sub.S (t)=x.sub.S (t)-x.sub.0 obtaining grating
phase error .delta..phi.(t)=2.pi..delta.x.sub.S /p, while undesired
stage rotation result in stage yaw error .delta..gamma..sub.S
(t)=.gamma..sub.S (t)-.gamma..sub.0 obtaining grating linewidth
variation .delta.L(t)=d.delta..gamma..sub.S (t), where p is the
grating period, d.sub.perp =d is the perpendicular image diameter,
and L.about.p/2 is the width of imaged grating lines. For best
results, stage lateral error .delta.x.sub.S needs to be controlled
such that .delta.x.sub.S <<p, or equivalently,
.delta..phi.<<2.pi., and stage yaw error .delta..gamma..sub.S
needs to be controlled such that .delta..gamma..sub.S <<p/d,
or equivalently, .delta.L<<L.
FIG. 7b depicts a distorted grating that would obtain due to
time-dependent lateral-path stage error during scanning. Stage 30
moves from top to bottom, causing grating image to appear to move
from bottom to top of substrate 17, writing grating stripe 359. At
an early time point image 359a moves along the desired path. At a
mid-time point, however, stage lateral error causes image 359b to
move a half-period to the right. At a late time point image 359c
moves back to the desired path. The result is a grating stripe with
an undesired position-dependent phase error. FIG. 7c depicts a
distorted grating that would obtain due to time-dependent stage yaw
error during scanning. Stage 30 moves from bottom to top, causing
grating image to appear to move from bottom to top of substrate 17,
writing grating stripe 360. At an early time point image 360a moves
along the desired path with zero yaw error. At a mid-time point,
however, stage yaw error causes image 360b to rotate clockwise. At
a late-time point image 359c has rotated back to the desired angle.
The result is a grating stripe with undesired position-dependant
linewidth variations.
With reference now to FIG. 8a, a general condition is described
which resolves the stage lateral path error problem by
phase-locking the grating image, generated by a single pair of
beams, to the stage during scanning. .phi..sub.L is defined as the
phase of the left beam 25 and .phi..sub.R as the phase of the right
beam 26. The phase difference between the beams is
.DELTA..phi.=.phi..sub.L -.phi..sub.R. With reference to FIG. 8b,
the interference of two beams on substrate 17 results in image 38
with fringes of period p=.lambda./(2 sin .theta.). The fringes will
appear to "walk" across the image with position x.sub.F
(t)=p.DELTA..phi./2.pi. and velocity u.sub.F (t)=dx.sub.F
/dt=p.DELTA.f, where .DELTA.f is the frequency difference between
the arms given by .DELTA.f=d.DELTA..phi.dt/2.pi.=f.sub.L -f.sub.R,
and where f.sub.L =d.phi..sub.L /dt/2.pi. is the frequency of the
left beam and f.sub.R =d.phi..sub.R /dt/2.pi. is the frequency of
the right beam. For this reason .DELTA..phi. is referred to as the
image phase and .DELTA.f as the image frequency. The condition
which ensures that the fringes are stationary in the reference
frame of the substrate is that the fringe position and velocity are
identical to the stage position and velocity, or x.sub.F
(t)=x.sub.S (t) and u.sub.F (t)=u.sub.S (t), respectively. Only for
a particular image phase .DELTA..phi.=.DELTA..phi..sub.K (t), or
equivalently, image frequency .DELTA.f=.DELTA.f.sub.K (t), called
the locked phase and locked frequency, respectively, will these
conditions hold. The relationship which ensures that the image is
phase locked to the stage is thus .DELTA..phi.=.DELTA..phi..sub.K
(t)=2.pi.x.sub.S (t)/p+C, where C is an arbitrary constant. The
image and stage may be thus synchronized using a variety of phase
measurement and control methods described hereinafter.
The substrate position (x.sub.S,y.sub.S,.gamma..sub.S) and velocity
(u.sub.S,v.sub.S,.omega..sub.S) are known to stage position-sensor
controller 35 with high accuracy in near real-time, and so are
available, in principle, to master controller 1 to calculate and
manipulate the phases of individual beams to ensure phase locking.
A number of ways may be used to measure and control the phase and
frequency of interferometer beams, including the use of
piezo-actuated mirrors, electro-optic and acousto-optic modulators,
and moving gratings. (For example, see E. H. Anderson, H. I. Smith,
and M. L. Schattenburg, "Holographic Lithography," U.S. Pat. No.
5,142,385.) However, previous usage has been to control the phase
or frequency of beams impingent on stationary substrates, rather
than on moving substrates described here. Detailed descriptions of
various ways to measure and control the phases of individual
interferometer arms are provided hereinafter. A specific means to
control the phase of the interferometer arms, and thus the image
phase, is depicted in FIG. 8c. Beam from laser 11 travels through
shutter/attenuator 12 and is split into right and left beams by
beamsplitter 14. Left and right beams are directed by mirrors 16 to
interfere at substrate 17. The phase of the right beam is
controlled by use of piezoelectric actuator 140, which is
controlled by controller 141, in turn controlled by master
controller 1. Actuator 140 pushes on mirror 16b, shortening the
length of the right arm and thus controlling the phase of the right
beam.
The phase-lock relationship described above is completely general
in that it holds for arbitrary scan paths. In particular, with
reference to FIG. 9, an alternative writing scheme is depicted in
which the stage scans perpendicular to the grating lines. In this
case, rather than requiring small phase shifts between the arms to
control the image phase in the parallel-scanning scheme depicted in
FIG. 5, this cross (or Doppler) scanning method requires rapid and
continuous phase shifts with time (i.e., frequency shifts) to
synchronize the fringes with the moving stage. In this case, rather
than discussing the phase difference between the arms,
.DELTA..phi.=.phi..sub.L -.phi..sub.R, it is more useful to use the
frequency difference .DELTA.f=f.sub.L -f.sub.R
=d.DELTA..phi./dt/2.pi.. The phase lock condition is given by
.DELTA.f=.DELTA..sub.K (t)=d.DELTA..phi..sub.K /dt/2.pi.=dx.sub.S
/dt/p=u.sub.S (t)/p. This condition ensures phase locking for
arbitrary scan paths and velocities.
The method of phase locking is now extended to multiple beam pairs.
Useful control over the intensity distribution of radiation within
the image can be achieved by employing multiple interfering beam
pairs in conjunction with beam scanning. According to the
well-known principles of Fourier optics (e.g., see J. W. Goodman,
Fourier Optics, McGraw Hill, 1968), any desired image can be
synthesized by a sum of mutually-coherent spatial frequency
components, each component achieved by interfering a pair of beams
with prescribed amplitude, phase, rotation angle, and azimuthal
angle. According to this principle, a desired image
spatial-frequency component corresponding to spatial frequency q,
or equivalently, period p=1/q, with rotation angle of fringes in
the x-y plane given by .psi., defined as the CCW angle between the
y axis and the image fringes, can be achieved by the use of a pair
of beams of equal amplitude and controlled phase, overlapping on
the substrate, where the beam's plane of incidence may be tilted
with respect to the z axis by an angle .zeta., and where the
desired azimuthal (intersection) half-angle of incidence .theta.
between the beams is obtained from the relationship p=.lambda./(2
sin .theta.), and where the rotation angle of the plane of
incidence about the z axis is given by .psi., defined as the CCW
angle between the x axis and the intersection of the plane of
incidence with the x-y plane. Preferred methods for creating and
controlling multiple beams pairs incident in multiple
interferometer planes are described hereinafter.
According to Fourier optics principles, general image synthesis
requires the set of image spatial frequency components {q} to be
mutually coherent (coherent imaging), such that each has a
prescribed phase with respect to other components, implying that
all beams have the same frequency f=c/.lambda. and thus the same
wavelength .lambda., where c is the speed of light The intensity of
the irradiance distribution on the surface of substrate 17 is then
determined by the square of the sum of the electric fields due to
all beams impingent on the image. It follows that spatial frequency
components created by beam pairs with frequencies, and thus with
wavelengths different from other beam pairs, cannot be mutually
coherent. In this case (incoherent imaging), the intensity of the
irradiance distribution on the surface of substrate 17 is
determined by the sum of the square of the electric fields due to
all beam pairs impingent on the image. The latter case is
equivalent to writing each spatial frequency component to the
substrate in separate writing passes.
It also follows from Fourier optics principles that a particular
writing interferometer configuration, corresponding to a particular
and restricted set of incident beam pairs with rotation angles
{.psi.} and azimuthal angles {.theta.}, can only be used to write a
correspondingly restricted set of spatial frequency components on
substrate 17. An expanded set of spatial frequency components can
be generated by performing multiple-pass writing to substrate 17,
wherein the substrate is rotated and/or the writing interferometer
is reconfigured between writing passes. While a much larger set of
useful patterns can be generated this way, the incoherent imaging
patterns are limited in two ways: (1) radiation from subsequent
passes cannot interfere coherently with previous-pass exposures,
limiting generality, and (2) the background level of exposure in
the resist tends to increase with multiple exposures, reducing
contrast. A. Fernandes and D. W. Phillion (Applied Optics, Vol. 37,
pp. 473-478, 1998) and S. H. Zaidi and S. R. J. Brueck (J. Vac.
Sci. Technol. B, Vol. 11, pp. 658-666, 1993) discuss many aspects
of multiple exposure interference lithography.
To enable general Fourier image synthesis, consider a writing
interferometer with K planes of incidence (POI), identified by
index j=1, 2, . . . , K, each plane j containing N.sub.j beam
pairs, identified by index i=1, 2, . . . , N.sub.j. The amplitudes,
phases, frequencies, azimuthal angles, and rotation angles out of
the POI of the left arm beams writing frequency components (i,j)
are given by .alpha..sub.L(i,j), .phi..sub.L(i,j), f.sub.L(i,j)
=d.phi..sub.L(i,j) /dt/2.pi., .theta..sub.L(i,j), and
.psi..sub.(i,j), respectively, and the amplitudes, phases,
frequencies, azimuthal angles, and rotation angles out to the POI
of the right arm beams are given by .alpha..sub.R(i,j),
.phi..sub.R(i,j), f.sub.R(i,j) =d.phi..sub.R(i,j) /dt/2.pi.,
.theta..sub.R(i,j), and .psi..sub.R(i,j), respectively. The POI
subscripts is generally suppressed for the case that all beams are
incident in a single plane of incidence (K=1), so that frequency
components are simply labeled with (i) and N.sub.j is simply
written N. The beam pair subscript i is further suppressed in the
case of a single pair of beams in a single plane of incidence.
To achieve maximum image contrast the amplitudes of the left and
right arms are generally set equal, or .alpha..sub.L(i,j)
=.alpha..sub.R(i,j). The image amplitude is defined as
.alpha..sub.(i,j) =.alpha..sub.L(i,j) +.alpha..sub.R(i,j)
=2.alpha..sub.L(i,j) =2.alpha..sub.R(i,j).
The image azimuthal angle is defined as .theta..sub.(i,j)
=(.theta..sub.L(i,j) +.theta..sub.R(i,j))/2, which measures the
angle between the arms, and tilt angle .theta..sub.T(i,j)
=(.theta..sub.L(i,j) -.theta..sub.R(i,j))/2, which measures the
tilt angle of the fringe planes with respect to the z axis. To
achieve optimal image period and phase control it is required that
the image fringes lie parallel to the substrate normal (z axis),
implying that .theta..sub.T(i,j) =0 or .theta..sub.L(i,j)
=.theta..sub.R(i,j).
The image rotation angle is defined as .psi..sub.j
=(.psi..sub.L(i,j) +.psi..sub.R(i,j))/2 and POI tilt angle
.zeta..sub.j =(.psi..sub.L(i,j) -.psi..sub.R(i,j))/.sup.2. It is
generally optimal to set .psi..sub.L(i,j) =.psi..sub.R(i,j),
implying that .psi..sub.j =.psi..sub.L(i,j) =.psi..sub.R(i,j) and
.zeta..sub.j =0.
The image periods p.sub.(i,j) resulting from angles
.theta..sub.(i,j) are given by p.sub.(i,j) =.lambda./(2 sin
.theta..sub.(i,j)). The phase difference between the beams in each
pair (relative image phase) is defined as .DELTA..phi..sub.(i,j)
=.phi..sub.L(i,j) -.phi..sub.R(i,j), and the relative frequency
difference (relative image frequency) with .DELTA.f.sub.(i,j)
=f.sub.L(i,j) -f.sub.R(i,j) =d.DELTA..phi..sub.(i,j) /dt/2.pi.. The
absolute image phase is defined as .chi..sub.(i,j)
=.phi..sub.L(i,j) and the absolute image frequency is defined as
.xi..sub.(i,j) =.xi..sub.L(i,j) =d.chi..sub.(i,j) /dt/2.pi..
Before general phase-locking conditions can be derived for
phase-locking multiple beam pairs in multiple planes of incidence,
necessary coordinate systems must be defined, interferometer
geometry, and grating parameters. A stage reference frame (x,y,z)
has been defined which is attached to rigid block 22. The
intersection point of the overlapping beams pairs (the image
center) typically occurs at coordinate x=y=z=0. In the stage frame
the moving position of the center of substrate 17 is defined as
x=x.sub.S (t), y=y.sub.S (t), and the substrate surface height at
the image center (at x=y=0) is defined as z=z.sub.S (t). Typically
x.sub.S =y.sub.S =z.sub.S =0 when substrate stage 30 is at the
center of its range of travel. The x-velocity u.sub.S (t)=dx.sub.S
/dt, y-velocity v.sub.S (t)=dy.sub.S /dt, and z-velocity w.sub.S
(t)=dz.sub.S /dt are also defined
A substrate reference frame is defined (X,Y,Z) which is attached to
substrate 17. This coordinate system is defined such that X=Y=Z=0
on the substrate surface at its geometric center. Substrate 17 is
chucked to rotation stage 30b, which is rigidly attached to, and
travels with, x-y stage 30. A yaw angle is defined,
.gamma.=.gamma..sub.S (t), of rotation stage 30b with respect to
substrate stage 30, such that .gamma..sub.S is the angle between
the x and X axis and increases as stage 30b rotates CW, implying
that x=X and y=Y when .gamma..sub.S =0. The rotary stage 30b spin
speed is defined with .omega..sub.S (t)=d.gamma..sub.S /dt.
The position (X.sub.B,Y.sub.B) of the image center on the substrate
surface, as measured in the substrate frame, which varies as the
stage moves, is obtained from the relations X=X.sub.B (t)=-x.sub.S
cos .gamma..sub.S +y.sub.S sin .gamma..sub.S and Y=Y.sub.B
(t)=-x.sub.S sin .gamma..sub.S -y.sub.S cos .gamma..sub.S (t) is
defined as the substrate surface height at the beam center. The
velocity of the image center (U.sub.B,V.sub.B) is obtained from the
relations U.sub.B (t)=dX.sub.B /dt=(x.sub.S.omega..sub.S +v.sub.S)
sin .gamma..sub.S +(y.sub.S.omega..sub.S -u.sub.S) cos
.gamma..sub.S and V.sub.B (t)=dY.sub.B /dt=(y.sub.S.omega..sub.S
-u.sub.S) sin .gamma..sub.S -(x.sub.S.omega..sub.S +v.sub.S) cos
.gamma..sub.S, and the substrate surface Z-velocity is obtained
from ##EQU1##
The map of substrate surface height is defined as Z.sub.W (X,Y). It
follows that z.sub.S (t)=Z.sub.B (t)=Z.sub.W (X.sub.B,Y.sub.B).
In general, before writing to substrate 17 can commence, a complete
description of the desired spatial frequency components at every
area of the substrate must be established. This can be defined by a
set of spatial frequency maps Q.sub.(i,j) (X,Y), or equivalently,
grating period maps P.sub.(i,j) (X,Y)=1/Q.sub.(i,j) (X,Y), each
corresponding to spatial frequency component (i,j) at substrate
frame location (X,Y). The corresponding half-angles of beams
writing frequency components (i,j) are determined from
.THETA..sub.(i,j) (X,Y)=sin.sup.-1 [.lambda./(2P.sub.(i,j))].
It is also necessary to define the desired maps of amplitudes
A.sub.(i,j) (X,Y), relative phases .PHI..sub.(i,j) (X,Y), absolute
phases .XI..sub.(i,j) (X,Y), and rotation angles .GAMMA..sub.j
(X,Y) of the fringes, for frequency components (i,j) observed in
the substrate frame, where .GAMMA..sub.j corresponds to the CCW
angle between the Y axis and the fringes for POI.sub.j. Since
angles .psi..sub.j are fixed, this requires the condition
.GAMMA..sub.j =.psi..sub.j -(.psi..sub.1 -.GAMMA..sub.1). For the
coherent imaging case, where all beam pairs have identical
frequencies in the substrate plane, the absolute phases
.XI..sub.(i,j) (X,Y) are necessary for complete image synthesis.
For the incoherent imaging case, where each beam pair has a unique
frequency in the substrate plane, the absolute phases are
meaningless and unnecessary.
An important task prior to writing to the substrate is to define a
specific scanning scheme designed to write the desired pattern with
uniform or otherwise controlled dose over a prescribed region of
sample 17. The functions X.sub.B (t) and Y.sub.B (t) define the
desired scan path, and U.sub.B (t)=dX.sub.B /dt and V.sub.B
(t)=dY.sub.B /dt the desired scan velocity, of the image on the
substrate, as measured in the substrate frame. For example, for
incoherent imaging, the energy dose absorbed in resist 18, for
frequency component (i,j), is given by ##EQU2##
where T is the time duration of exposure and G.sub.(i,j) (X,Y) is
the intensity profile of the Gaussian beams projected onto the
substrate. A well-controlled dose is ensured by the selection of a
scan path with controlled velocity and tightly overlapped scans,
such as the boustrophedonic pattern depicted in FIGS. 5 and 9. Loss
of dose control caused by image velocity variations during scanning
can be compensated by, changes in beam amplitudes
.alpha..sub.(i,j).
At every point (X.sub.B,Y.sub.B) on substrate 17 during scanning,
where it is desired to write the image following the scan path, the
substrate stage must be rotated and translated to bring the desired
substrate region under the fixed image at the proper angle. First,
the image fringes are aligned to the desired fringe direction on
substrate 17 by continuously rotating the stage frame to the locked
angle .gamma..sub.S =.gamma..sub.K (t)=.psi..sub.j +.GAMMA..sub.j
(X.sub.B,Y.sub.B), and with locked spin ##EQU3##
The substrate stage is also simultaneously and continuously
translated to locked position x.sub.S =x.sub.K (t)=-X.sub.B cos
.gamma..sub.K -Y.sub.B sin .gamma..sub.K and y.sub.S =y.sub.K
(t)=X.sub.b sin .gamma..sub.K -Y.sub.B cos .gamma..sub.K, and with
locked velocity ##EQU4##
Also at every point (X.sub.B,Y.sub.B) on the substrate 17 during
scanning, the amplitudes and angles of the incident beams need to
be determined and controlled. Generally, fringe contrast is
maximized when the amplitudes of left and right arms are equal
(.alpha..sub.L(i,j) =.alpha..sub.R(i,j)), so during writing the
locked amplitude is set .alpha..sub.(i,j) =.alpha..sub.K(i,j)
(t)=A.sub.(i,j) (X.sub.B,Y.sub.B). At every point (X.sub.B,Y.sub.B)
the desired periods P.sub.(i,j) (X,Y) have been defined. In
practice, the image period p.sub.(i,j) is set equal to the locked
period p.sub.(i,j) =p.sub.K(i,j) =P.sub.(i,j) (X.sub.B,Y.sub.B) by
setting the image angle .theta..sub.(i,j) to the locked angle
.theta..sub.(i,j) =.theta..sub.K(i,j) =.THETA..sub.(i,j)
(X.sub.B,Y.sub.B).
The expressions for locking the image phases and frequencies to
moving substrate 17 are, now derived. While following the scan path
with substrate positions [X.sub.B (t),Y.sub.B (t)], and surface
height Z.sub.B (t), the relative image phase,
.DELTA..phi..sub.(i,j), is set equal to the locked relative image
phase .DELTA..phi..sub.K(i,j) with the relation
.DELTA..phi..sub.(i,j) =.DELTA..phi..sub.K(i,j) (t)=.PHI..sub.(i,j)
(X.sub.B,Y.sub.B). The equivalent condition for locking the
relative image frequency is .DELTA.f.sub.(i,j) =.DELTA.f.sub.K(i,j)
(t)=d.PHI..sub.(i,j) /dt/2.pi.=Q.sub.(i,j)
(X.sub.B,Y.sub.B)[U.sub.K (t) cos .GAMMA..sub.j +V.sub.K (t) sin
.GAMMA..sub.j ]. Also while following the scan path, the absolute
image phase, .chi..sub.(i,j), is to set equal to the locked
absolute image phase, .chi..sub.K(i,j), with the relation
##EQU5##
The equivalent condition for locking the absolute image frequency
is ##EQU6##
For many applications it is desirable to limit the rapidity that
grating parameters change during scanning so that minimal image
smearing occurs. Overly rapid changes of image period, phase, or
rotation will cause loss of grating phase fidelity and/or contrast,
necessitating either a smaller image size or modification of the
grating design to reduce the rapidity of grating parameter changes
across the substrate. The optimal conditions for grating parameter
changes per image diameter are as follows: phase change
.DELTA..phi.<<2.pi.; period change .DELTA.p<<p.sup.2
/d.sub.par ; image rotation .DELTA..psi.<<p/d.
For illustrative purposes, FIG. 10a depicts a couple of beam pairs
incident in the same plane (.psi..sub.1 =.psi..sub.2). Left beam
#125b has phase .phi..sub.L(1), frequency f.sub.L(1), and azimuthal
angle .theta..sub.(1) ; right beam #126b has phase .phi..sub.R(1),
frequency f.sub.R(1), and azimuthal angle .theta..sub.(1) ; left
beam #225a has phase .phi..sub.L(2), frequency f.sub.L(2), and
azimuthal angle .theta..sub.(2) ; right beam #226a has phase
.phi..sub.R(2), frequency f.sub.R(2), and azimuthal angle
.theta..sub.(2). An interferometer illustrating a simple embodiment
of the phase locking principle is depicted in FIG. 10b.
Transmission grating 50 has been designed to split beam from laser
11 into a zero order beam which is blocked by stop 52, a pair of
first-order diffracted beams which are directed to substrate 17 by
mirrors 76, where they interfere with azimuthal angle
.theta..sub.(1), and a pair of second-order diffracted beams which
are also directed to substrate 17 by mirrors 75, where they
interfere with azimuthal angle .theta..sub.(2). Thus the image
comprises two distinct spatial frequency components with periods
p.sub.(1) =.lambda./(2 sin .theta..sub.(1)) and p.sub.(2)
=.lambda./(2 sin .theta..sub.(2)). In this example, the phase and
amplitude of the two spatial frequency components are controlled by
laborious design and fabrication of beamsplitter 50 and tedious
adjustment of mirrors 75 and 76. Alternative interferometer designs
are described hereinafter which allow more general and rapid
control of the spatial frequency components in the image.
Most writing interferometer designs described herein are readily
generalized to multiple planes of incidence. In the case of the
interferometer depicted in FIG. 10b, beamsplitter grating 50, which
is depicted in FIG. 10c as viewed along the -z direction, consists
of a grating deposited or etched into a transparent substrate. In
this particular example grating 50 is designed to diffract the
incident beam into a zero order and .+-.1 and .+-.2 order beams in
the x-z plane. Alternatively, grating beamsplitter 50 can be
replaced with grid beamsplitter 50b, depicted in FIG. 10d. Grid 50b
is designed to diffract the incident beam into 9 beams: zero order,
.+-.1 and .+-.2 orders in the x-z plane, and .+-.1 and .+-.2 orders
in the x-y plane. Additional mirrors, similar to mirrors 75 and 76
in FIG. 10b, are required to direct the beams diffracted in the y-z
plane to intersect on substrate 17.
A few examples of useful images that can be achieved by summing
multiple beam pairs are depicted in FIG. 11. FIG. 11a depicts a
grating image with equal lines and spaces achieved by interfering a
single beam-pair. FIG. 11b depicts a grating image of the same
period but with thin lines achieved by interfering two beam-pairs
incident in the same plane. FIG. 11c depicts a grating image of the
same period but with even thinner lines achieved by interfering
three beam pairs incident in the same plane. FIG. 11d depicts a
grid image achieved by interfering two beam pairs, each pair
incident with the same angle .theta. but in a different plane of
incidence separated by 90 degrees (i.e., .psi..sub.2 -.psi..sub.1
=90 degrees; see A. Fernandez and D. Phillon, "Effects of phase
shifts on four-beam interference patterns," Appl. Optics 37,
473-478 [1998]).
These principles may be used to pattern precision periodic
structures on many types of substrates or other objects, including
optical fibers and information storage disks. With reference to
FIG. 12, a scheme is depicted for patterning gratings onto the
cores of optical fibers. Such gratings are used for filtering and
other manipulations of light beams in fibers commonly used in
high-speed fiber-optic communications. In this scheme, a writing
interferometer (not shown) directs and interferes left beam 25 of
frequency f.sub.L and right beam 26 of frequency f.sub.R, with
controlled frequency difference between the beams, .DELTA.f=f.sub.L
-f.sub.R, forming an image on the fiber with period p=.lambda./(2
sin .theta.). Feed spool 63a feeds optical fiber 62 to pickup spool
63b such that the speed of the fiber past the image is u.sub.S (t).
The grating is then inscribed onto the fiber while satisfying the
phase lock condition .DELTA.f.sub.S =.DELTA.f.sub.K =u.sub.S (t)/p.
Alternatively, spools 63a and 63b can be attached to an x-y table,
such that short sections of fiber are paid out and the spools
locked, and the grating is written by subsequently moving the stage
in the x-direction with speed u.sub.S (t), while satisfying the
phase lock condition.
With reference now to FIG. 13, a scheme is depicted for pattering
periodic structures onto information storage media such as magnetic
or optical disks. In particular, with reference to FIG. 13a, a
writing interferometer (not shown) directs and interferes left beam
25 of frequency f.sub.L and right beam 26 of frequency f.sub.R,
with controlled frequency difference .DELTA.f=f.sub.L -f.sub.R,
forming an image on the disk at radius R with period p=.lambda./(2
sin .theta.). Disk 64 is spun with angular frequency .omega..sub.S,
such that the speed of the media under the image is R.omega..sub.S.
The grating is then inscribed onto the disk while satisfying the
phase lock condition. FIG. 13a depicts a grating that would obtain
if the plane of incidence of the pair of writing beams were
perpendicular to the direction of motion of the media under the
image, yielding the phase lock condition .DELTA.f=0. FIG. 13b
depicts a grating that would obtain if the plane of incidence of
the pair of writing beams were parallel to the direction of motion
of the media under the image, yielding the phase lock condition
.DELTA.f=R.omega..sub.S /p. FIG. 13c depicts a grid that would be
obtained if two pairs of writing beams were used: one that is
parallel to the direction of motion of the media under the image,
and one that is perpendicular.
The description of ways interference lithography (IL) can be
performed on moving substrates by using the method of phase locking
has now been provided. Further benefits of narrow beams in IL, and
a number of ways the beams could be split and recombined on a
substrate, generating image periods both statically and under
electronic control will now be provided. With reference to FIG. 14,
the method for splitting and recombining beams, depicted earlier in
FIGS. 1-3, is examined in further detail. In particular, with
reference to FIG. 14a, beam from laser 11 passes through
shutter/attenuator 12 and is then spatially filtered by means of
focusing lens 85, pinhole 86, and collimating lens 87. The spatial
filter ensures good wavefront quality of the beam (flat phase),
which will nominally ensure that the interferometer image has
straight grating lines. The beam is then split into left and right
beams by dielectric beamsplitter 14. Left beam is adjusted by
attenuator 15 in order to balance the intensity of both
interferometer arms, and is then directed to substrate 17 by left
mirror 16a. Right beam is directed to the substrate by right mirror
16b. Substrate 17 is attached to x-y stage 30, to which is attached
interferometer reference mirror 43. Stage 30 is
interferoinetrically controlled and scanned, as described
previously. FIG. 14b depicts a grating image that would obtain if
spatial filter 85-87 had been designed to transmit a beam of large
diameter to beamsplitter 14. A large distortion is evident in the
image, which represents the combined optical manufacturing figure
errors in the regions sampled by the beam due to beamsplitter 14,
attenuator 15 and mirrors 16. However, if spatial filter 85-87 is
designed to transmit a beam of smaller diameter, then a smaller
region of the optical components will be sampled and an image with
reduced distortion, such as depicted in FIG. 14c, will result.
FIG. 15a depicts an alternative method for forming the image. In
this case the beam is spatially filtered after the beamsplitter and
mirrors, rather than before. Beams from mirrors 16 are focused by
lenses 95 onto pinholes 96 and are then allowed to expand to
substrate 17 without the use of collimating lenses. Alternatively,
FIG. 15b depicts a method which avoids the use of recombiner
mirrors 16, but rather uses focusing lenses 55 to direct the light
into optical fibers 56, which are then bent to direct the light to
substrate 17. In both these cases, light propagating from the
pinhole or fiber will expand as spherical wavefronts to the
substrate, forming an image with hyperbolic distortion, as depicted
in FIG. 15c. However, by the use of spatial filters or fibers
designed to propagate narrow beams, a smaller image with reduced
distortion can be achieved, as depicted in FIG. 15d.
FIG. 16a depicts an interferometer similar to that depicted in FIG.
15a, except that collimating lenses 97 have been used to produce
flat wavefronts rather than spherical ones. If high quality lenses
97 are used, a low-distortion image depicted in FIG. 16b will be
obtained. The advantage of this design is that other optical
components of the system do not have to be of such high quality,
since spatial filters 95-97 remove wavefront aberrations caused by
these components.
FIGS. 17-18 depict interferometer designs that avoid the use of
recombiner optics, but instead place the substrate in the near
field of a diffractive beamsplitter. With reference to FIG. 17a,
beam from laser 11 is directed normally to transmission-grating
beamsplitter 50, also called a phase mask, which produces
diffracted left (-1 order) and right (+1 order) beams. Beamsplitter
50 is designed to suppress zero-order diffraction, transmitting
only .+-.1 orders. Diffracted beams are incident on substrate 17,
which is chucked to stage 30 and controlled as described
previously. Details of the near-field diffraction region are
depicted in FIG. 17b. Left and right diffracted beams overlap and
interfere in small region 27 near the phase mask, casting a grating
image in resist 18 on substrate 17. Substrate 17 needs to be placed
close to mask 50 such that resist 18 samples a substantial portion
of interference region 27.
An alternative near-field interferometer design is depicted in FIG.
18. With reference to FIG. 18a, beam from laser 11 is directed to
beamsplitter 50 as before, but in this case at an angle such that
the zero- and -1-order beams diffract from mask 50 at the same
angle with respect to the normal. Mask 50 is designed to transmit
zero- and -1-order beams of equal intensity, while suppressing the
+1 order beam. Details of the near-field diffraction region are
depicted in FIG. 18b. Image formation occurs in an identical
fashion as depicted in FIG. 17.
With reference now to FIG. 19a, an achromatic interference
lithography design is depicted (see T. A. Savas, M. L.
Schattenburg, J. M. Carter, and H. I. Smith, "Large-area achromatic
interferometric lithography for 100 nm period gratings and grids,"
J. Vac. Sci. Technol. B 14, 41674170 (1996)). This design is very
tolerant of beam spatial and temporal incoherence. Beam from laser
11 is reflected from optional mirror 13 and travels through
shutter/attenuator 12. Beam then transmits through splitter grating
50, diffracting into zero and .+-.1 orders. Zero-order beam is
blocked by stop 52. The intensity of left beam is balanced with
right beam by use of attenuator 15. Beams are then directed to
recombiner gratings 51, which direct -2-order diffracted beams to
substrate 17, where they interfere to form grating image. Zero and
+1-order beams from gratings 51 are blocked by stops 53.
An alternative means to recombine beams is depicted in FIG. 19b.
Diffracted beams from splitter grating 50 are refracted and focused
by lens 70, which directs them to substrate 17, where they overlap
and interfere to form grating image. This design has the advantage
that rapid changes of writing grating period, which is determined
by the 20 angle between the interfering beams, may be effected
simply by changing the period of beamsplitter 50. However, beams
combined by lens 70 will have significant phase curvature due to
focussing, resulting in an image with undesirable hyperbolic
distortion. An improved design, which avoids this problem, is
depicted in FIG. 19c. Beam from laser 11 is split by grating 50, as
described previously, but in this case beams are directed by lens
71 to aperture plate 72, which lies at the focus of lens 71. The
beams then expand to second lens 70 that directs them to substrate
17, where they overlap and interfere. Lens 70 performs two
functions: (1) collimating the expanding beams from aperture plate
72, and (2) recombining the beams at the substrate. Lens 70,
aperture plate 72, and lens 71 are collectively referred to as an
objective lens.
Aperture plate 72 may be designed to spatially filter the beams,
and can take many forms depending on the application. For example,
FIG. 19d depicts a first aperture plate 72a with discrete holes for
the -1 order 73a and +1 order 73b. The size of the holes and their
spacing in aperture plate 72 would be determined by the beam
diameter at focus and the desired period of the writing grating.
Holes thus designed would only allow beams of the desired spatial
frequency to propagate through the objective lens and impinge on
the substrate, blocking other beams generated, for example, by
imperfections in the optics. FIG. 19e depicts a second aperture
plate 72b with a slit opening 74 rather than discrete holes. In
this case, spatial filtering is only performed on spatial
frequencies in the y direction. The advantage in this case is that
aperture plate 72b does not need to be changed if the period of
splitter grating 50 is changed. FIG. 19f depicts a third aperture
plate 72c which would be used in the case that grating splitter 50
is replaced with a grid beamsplitter similar to 50b depicted in
FIG. 10d. In this case .+-.1 order beams are diffracted in both the
x-z and y-z planes. Holes 73a and 73b in aperture plate 72c provide
spatial filtering of the .+-.1 beams diffracted in the x-z plane,
and holes 73c and 73d provide filtering of the .+-.1 beams
diffracted in the y-z plane. FIG. 19g depicts a fourth aperture
plate 72d that would also be used in the case of a grid
beamsplitter similar to that used in the case depicted in FIG. 19f.
Cross-shaped slit 77 provides spatial filtering of all beams
diffracted along the x-z and y-z planes, with similar benefits as
in the case depicted in FIG. 19e.
The enumeration of ways that narrow beams may be split and
recombined to form grating images of static period has been
provided. Several methods where the period of the grating may be
varied continuously (or "chirped"), while writing, under electronic
control will now be provided. These methods may be used to write
substrates with constant grating period, but where rapid changes of
grating period between substrates is desired, or they may be used
to write gratings where the period is intended to vary continuously
across the substrate in a controlled fashion. The geometric
requirements for continuous phase, period, and rotation of the
image during writing to the substrate were described heretofore.
Here a couple of examples of practical application of these
concepts are illustrated.
With reference to FIG. 20a, a scanning scheme for writing gratings
with period varying in one dimension is described. Substrate 17 is
chucked to x-y stage 30 described previously, and scanned in a
boustrophedonic fashion, similar as described previously and
depicted in FIG. 5, writing variable-period grating 39. Scanning
starts with image 48a of period p.sub.1 in lower left-hand corner
of substrate. Stage 30 scans in the -y direction traversing the
substrate, while fixing x. Stage 30 is then stopped and the writing
interferometer is reconfigured such that image 48b has grating
period p.sub.2 =p.sub.1 +.DELTA.p, where .DELTA.p is small compared
to p.sub.1. Stage 30 is then moved in the -.DELTA.x direction,
where .DELTA.x is a fraction of the beam diameter, say 10-50%,
while simultaneously being an exact multiple of distance (p.sub.1
+p.sub.2)/2. Stage 30 then scans in the +y direction traversing the
substrate, while fixing x. The procedure is then repeated with
image 48c of grating period p.sub.3, etc., until the desired area
of substrate 17 has been written. Alternatively, the substrate may
be written with a Doppler-scanning scheme similar to that described
previously and depicted in FIG. 9, where the stage moves in a
direction perpendicular to the grating lines and the grating period
is varied continuously while scanning while satisfying the same
conditions.
With reference to FIG. 20b, a scanning scheme for writing gratings
with period both varying and rotating is described. Substrate 17 is
chucked to rotation stage 30b which is supported by x-y stage 30
described previously, and scanned in a boustrophedonic fashion in
the frame of the substrate, similar as described previously and
depicted in FIG. 20b, writing variable-period grating 39. During
scanning, at every point on substrate 17, stage 30b .gamma..sub.S
rotary position, stage 30 x.sub.S and y.sub.S positions, and the
period, intensity, and phase in image 38 are varied and controlled
as described previously to write the desired grating pattern
39.
With reference to FIG. 21, a writing interferometer design is
depicted which allows continuous control of grating period. Beam
from laser 11 transmits through shutter/attenuator 12 and is split
by beamsplitter 14. Left and right beams are directed by mirrors 16
to substrate 17, where they overlap and interfere. Mirrors 16 are
attached to motorized stages 98, which allow translation and
rotation in the x-z plane. Stages 98 can be continuously adjusted
to overlap beams on substrate 17 within a range of intersection
angles 2.theta., corresponding to a range of grating periods.
Although the interferometer depicted in FIG. 21 meets the minimum
requirements for writing chirped gratings, it suffers from two
major problems: (1) only a limited range of angles 2.theta. are
accessible, and (2) period changes are slow and tedious to effect
due to the required six degrees of freedom of stages 98 and the
synchronization required to simultaneously overlap and control
beams at substrate 17 while achieving a desired period and phase.
An improved interferometer design, which avoids these difficulties,
is depicted in FIG. 22. With reference to FIG. 22a, beam from laser
11 travels through shutter/attenuator 12 and reflects from scanning
mirror 199. Mirror 199 can be rotated about the y-axis under
control of actuator 191 and actuator controller 141. Actuator 191
could be any type of electro-mechanical device that can be used to
rotate a mirror, such as a DC or stepper motor, piezoelectric,
electrostrictive, magnetostrictive, or galvanometer actuator. In
this design, the rotation of mirror 199 controls the beam 2.theta.
angle at the image on substrate 17, thus enabling simple and rapid
period changes. In particular, for the purpose of clarity, in the
figure are shown two possible beam paths through the interferometer
among the many paths available, corresponding to two different
grating periods: one case depicted by a dashed line corresponding
to azimuthal angle .theta..sub.(1), and the other by a solid line
corresponding to azimuthal angle .theta..sub.(2). Following now
from scanning mirror 199, the beam is focussed by lens 198 onto
mirror beamsplitter 185, which is described in detail below and
depicted in FIG. 22d. The mirror beamsplitter has the useful
property that beams impingent on the optic and offset from the
input optic axis, as shown in the figure (dot-dashed line), appear
at the output along with a corresponding mirror beam of the same
amplitude on the opposite side of the exit optic axis, as shown.
The beams then travel to lens 195, forming an image. An objective
lens, comprising lens 71, aperture 72, and lens 70, reforms the
grating image onto substrate 17.
Alternative means of deflecting beam from laser 11, rather than
using actuated scanning mirror 199, are now described. With
reference to FIG. 22b, beam from laser 11 transmits through
shutter/attenuator 12 and reflects from optional turning mirror 13,
impinging on electro-optic deflector (EOD) 10, controlled by EOD
controller 151, which deflects the transmitted beam through a range
of angles. The EOD is a well-known electro-optic device that
incorporates a specially designed crystal 10 to which are attached
metal plates 2. Voltage from controller 151 applied to plates 2
creates electric fields in the crystal, which cause a refractive
index gradient and thus angular deflection of the incident beam
(see A. Yarif and P. Yey, Optical Waves in Crystals,
Wiley-Interscience, 1984). Beam angular deflection is proportional
to applied voltage to a good approximation. In the figure an
undeflected (zero voltage) beam is indicated by a solid line, and a
typical deflected beam by a dashed line.
Alternatively, with reference to FIG. 22c, beam from laser 11 of
frequency f.sub.0 transmits through shutter/attenuator 12 and
reflects from optional turning mirror 13, impinging onto
acousto-optic deflector (AOD) 7, controlled by AOD controller 83,
which deflects the beam through a range of angles. The AOD is a
well-known electro-optic device which uses specially designed
crystal 7 to which is attached piezoelectric transducer 8 (see A.
Yarif and P. Yey, ibid.). Controller 83 sends a set of
radio-frequency (RF) signals of frequency {F.sub.(i) } to
transducer 8, which causes sound waves 19 of velocity S and
wavelengths .LAMBDA..sub.(1) =S/F.sub.(i) to propagate through the
crystal, where subscript index i=1,2, . . . , N indicates that N
distinct sound frequencies may be propagated. (This may be
generalized for K planes of incidence, as described later.) FIG.
22c depicts the special case N=2, so that .LAMBDA..sub.(2)
=S/F.sub.(1) and N.sub.2)=S/F(.sub.2). Light propagating through
the crystal at approximate right angles to the sound beam will be
diffracted into a zero order beam of frequency f.sub.0 and
first-order beams of frequency f.sub.(1) f=.sub.0 +F.sub.(1), by
the well-known principle of Bragg diffraction. The Bragg condition
must hold for efficient diffraction, which stipulates that the
angle of incidence of the incoming light beam to the acoustic
wavefronts must approximately equal the exit angle of the outgoing
first-order diffracted beam to the acoustic wavefronts. The angle
of deflection of the first-order beams to the zero-order beam is
given by .theta..sub.B(i) =.lambda.F.sub.(i) /S. In the figure two
deflected beams are depicted. The zero-order beam of frequency
f.sub.0 is indicated by a solid line, blocked by stop 9, a
first-order beam of frequency f.sub.(1) generated by RF frequency
F.sub.(1) by a short dash line, and a first-order beam of frequency
f.sub.(2) generated by RF frequency F.sub.(2) by a long dash
line.
In principle, AOD devices used in this manner control image period
p=.lambda./(2 sin .theta.) in two ways. First, by the change of the
angle .DELTA..theta.=.DELTA.F.lambda./S due to changes .DELTA.F of
RF frequency F. Secondly by the change of wavelength
.DELTA..lambda. due to changes in the frequency of the deflected
light .DELTA.f=.DELTA.F by virtue of the relationship .lambda.=c/f,
where c is the speed of light. From these considerations one
obtains the relationships
.DELTA.p/p=.DELTA..lambda./.lambda.=.DELTA.f/f=.DELTA.F/f For
example, typical AOD RF frequency shifts .DELTA.F are 20 MHz, while
V light of wavelength .lambda.=351.1 nm has a frequency
f=c/.lambda..about.800 THz, yielding
.DELTA.p/p.about.2.times.10.sup.-8. This is an extremely small
period variation that can safely be ignored when calculating and
controlling image periods during writing. For this reason, the
change of wavelength due to frequency changes has not been carried
into the equations posed earlier which describe methods of active
period control while writing. However, the fact that with AOD
optics the different spatial frequencies in the image are due to
beams of different temporal frequencies implies that only
incoherent imaging applies, as discussed earlier.
With reference to FIG. 22d, mirror beamsplitter 185, mentioned
previously and referred to in FIG. 22a, is described. The mirror
beamsplitter is used to split a beam (or set of beams) into a
mirrored parallel pair(s) of beams. It has the property that halves
of mirrored beam pairs traveling through the optic have the same
pathlength.
For simplicity, a single beam is depicted in the figure travelling
in the -z direction and incident on beamsplitter cube 190. "Cube
centerlines" are defined which bisect cube 190 with a y-z plane and
cube 194 with a x-z plane. Right beam transmitted through cube 190
is reflected through a downward excursion (y direction) in an x-y
plane by mirrors 192a-d. Left beam is reflected from cube 190
through an upward excursion (-y direction) in a y-z plane by
mirrors 193a-d. Phase difference between left and right beams may
be controlled by pushing on any of mirrors 192 or 193 with an
actuator. The utility of phase control between the interferometer
arms will be demonstrated hereinafter. The left and right beams are
combined into parallel non-overlapping beams travelling in the -x
direction, and in an x-y plane, by beamsplitter cube 194. The
function of the up and down excursions in the counterposing arms is
to create a parallel pair of beams travelling in the -x direction,
after cube 194, which move away from each other in the
.+-.y-direction (mirror images about cube 194 centerline) as the
beam incident on cube 190 moves away from the cube centerline in
the .+-.x-direction in an x-z plane. Optional fold mirrors 196 and
197 transfer the output beams from an x-y plane to an x-z plane,
simply for the convenience of referencing drawing 22a.
An alternative writing interferometer design is depicted in FIG.
23. The advantage of this design over the mirror interferometer
described previously, and depicted in FIG. 22, is the improved
control of the angle, amplitude and phase of the individual
interferometer arms, the benefits of which will become clear. With
reference to FIG. 23a, beam from laser 11 passes through
shutter/attenuator 12 and reflects from optional turning mirror 13
to beamsplitter 5, splitting into left and right beams.
Alternatively, cube beamsplitter 5 may be substituted with a flat
beamsplitter, or a transmission or reflection grating. Left and
right beams reflect from turning mirrors 6 and impinge on
electro-optic deflectors (EOD) 10, described previously.
Alternatively, beam deflectors 10 may be mechanically actuated
mirrors or acousto-optic deflectors, as described previously and
depicted in FIG. 22. Phase may be controlled by pushing either
mirrors 6 with an actuator. Left and right beams are superimposed
into a common diverging path by flat beamsplitter 3, which has been
designed with optional reflective surface 4 on the right half.
Alternatively, beam superimposer 3 may be a cube beamsplitter.
Alternatively it may be shortened such that beams from deflector
10a travel to lens 71 unimpeded, while beams from deflector 10b
reflect from The shorted mirror. Alternatively, it may be a
reflection or transmission grating as depicted in FIG. 23c and
described below. The resulting virtual image is projected onto
substrate 17 by the objective lens, comprising lens 71, aperture
72, and lens 70.
The purpose of beamsplitter 3 is to create a virtual grating image
from the superposition of the left and right beams. Voltage applied
to the EOD by controller 151 effects a range of angles, represented
in the figure by a solid line for a beam path corresponding to
angle 2.theta..sub.(max) near the lens NA limit, and by a dotdash
line for angle 2.theta..sub.(min) near zero. Large 2.theta. angles
correspond to the finest periods that may be written, while small
2.theta. angles correspond to periods that approach the size of the
beam. The use of optional reflective coating 4 on beamsplitter 3
improves the efficiency of the system since nearly all light from
the right arm may be projected onto substrate 17; however, its use
precludes the writing of gratings with periods approaching the size
of the beam, due to beam clipping near zero angle.
The writing interferometer depicted in FIG. 23a directs beams to
interfere on substrate 17 in a single plane of incidence. Replacing
beamsplitter 5 with a transmission or reflection grating or
holographic beamsplitter that generates multiple pairs of beams may
generate additional planes of incidence. Each beam generated this
way is redirected and deflected by a mirror and EO deflector
similar to as shown in FIG. 23a, where the members of beam pairs
are arranged opposite to each other around the optical axis. The
deflected beams are directed to converge and reflect from a
multi-faceted prism replacing beamsplittcr 3, where the prism has
one facet pair for every beam pair. This prism is a generalization
of prism 272 seen in FIG. 24c. Beam pairs reflecting from this
prism appear to diverge from a common point, similar to as depicted
in FIG. 23a.
Substituting AO deflectors for EO deflectors, in the design
depicted in FIG. 23a, enables the generation of multiple spatial
frequency components in the image. With reference to FIG. 23b, beam
from laser 11 of frequency f.sub.0 travels through shutter 12,
reflects from turning mirror 13, and is split by beamsplitter 5
into left and right beams which are diffracted by AO deflectors 7.
Right AOD 7b receives a set of RF signals {F.sub.R(i) } from
controller 83, generating diffracted beam(s) of frequencies
f.sub.R(i) =f.sub.0 +F.sub.R(i), and left AOD 7a receives
frequencies {F.sub.L(i) }, generating diffracted beam(s) of
frequencies f.sub.L(i) f.sub.0 +F.sub.L(i), where i=1,2, . . . N.
Using the principles discussed previously, this allows complete
control of the angles .theta..sub.(i), amplitudes .alpha..sub.(i),
and phases .phi..sub.(1) of every spatial frequency component in
the image.
Note that the design depicted in FIG. 23b constitutes an incoherent
imaging system, as discussed previously, since each spatial
frequency component, identified by angle .theta..sub.(i), is
generated by a beam pair with a different temporal frequency. Also
note that this design is easily generalized to provide more than
one plane of incidence by the use of multiple pairs of
acousto-optic modulators corresponding to multiple planes of
incidence, where the multiple incident planes are joined by the use
of additional beam superimposers similar to beamsplitter 3 but
oriented at other rotational angles.
An alternative method for superimposing beams, performing the same
functionality as plate beamsplitter 3 in FIGS. 23a, and 23b, is
depicted in FIG. 23c. The advantage of this design is higher
efficiency without the problem of not being able to approach the
largest spatial frequencies due to occultation of reflective
coating 4 on beamsplitter 3, as suffered by designs depicted in
FIGS. 23a and 23b. Other than the improved beam combiner, this
optical system is used in an identical fashion as the system
depicted in FIG. 23b. With reference to FIG. 23c, beam from laser
11 passes through shutter/attenuator 12 and reflects from optional
turning mirror 13 to transmission grating 50, splitting into left
-1-order, right +1-order, and zero-order beams. Zero order is
blocked by stop 52. Alternatively, grating 50 may be substituted
with a cube or flat beamsplitter, or a reflection grating. Left and
right beams reflect from turning mirrors 6 and impinge on
acousto-optic deflectors (AOD) 10, described previously.
Alternatively, beam deflectors 10 may be mechanically actuated
mirrors or electro-optic deflectors, as described previously and
depicted in FIG. 22. Diffracted and deflected beams from AOD 7
impinge on transmission grating 278. Alternatively, a reflection
grating may be used. In FIG. 23c, the full range of deflection of
the beams from AOD 10 is depicted by dashed line rays which are
diffract to the optical axis by grating 278, and by solid line rays
which diffract to the maximum angle of the system. Grating 278 is
designed to have weak zero order diffraction and strong first order
diffraction. Furthermore, beams from AOD 7 impinge on grating 278
at a steep angle such that the +1-order is cutoff, resulting in
strong -1-order diffraction which travels through beam stop 279 to
the objective lens, forming an image on substrate 17 in a manner
identical to depictions in FIGS. 23a and 23b. Beam stop 279 is
positioned to block all orders except -1-order diffraction from
grating 278.
The writing interferometer depicted in FIG. 23c directs beams to
interfere on substrate 17 in a single plane of incidence. Replacing
grating 50 with a transmission or reflection grating or holographic
beamsplitter that generates multiple pairs of beams may generate
additional planes of incidence. Each beam generated this way is
redirected and deflected by a mirror and AO deflector similar to as
shown in FIG. 23c, where the members of beam pairs are arranged
opposite to each other around the optical axis. The beams are
directed to converge and reflect from a multi-angled grating
beamsplitter that replaces grating beamsplitter 278. This
multi-angled beamsplitter is composed of multiple superimposed
gratings each with a roll angle corresponding to a particular beam
pair, in a generalization of grating 278 shown in FIG. 23c. Beam
pairs reflecting from this grating appear to diverge from a common
point, similar to as depicted in FIG. 23c. Apertures 279 or 72
block undesired higher-order beams.
An alternative interferometer design depicted in FIG. 24a has the
advantage of being more compact than the one depicted in FIG. 23.
It uses a single AOD of unusual design. Beam from laser 11 of
frequency f.sub.0 reflects from optional turning mirror 13 and
transmits through shutter/attenuator 12, impinging on AOD 79. AOD
79 consists of a single crystal with specially cut facets, to which
are bonded piezo-electric transducers 80. RF signals from
controller 83 with frequencies {F.sub.R(i) } applied to right
transducer 80a, and frequencies {F.sub.L(i) } applied to left
transducer 80b, launch counter-propagating sound waves 81. The
zero-order beam is blocked by stop 52, and left and right
diffracted first-order beams are imaged onto substrate 17 by
objective lens 70-72.
As described previously, the angle of deflection of a first-order
beam from the zero order is given by .theta..sub.B(i)
=.lambda.F.sub.(i) /S, where .lambda. is the optical wavelength,
F.sub.(i) is the sound frequency, and S is the sound velocity. AOD
typically have an angular bandwidth around .theta..sub.B of
approximately 10-20% within which efficient diffraction occurs.
This corresponds to a range of RF frequencies, diffracted angles,
and image periods, depicted in the figure as a solid line and
frequency with subscript (min) for beams corresponding to the
minimum image period specified by angle .theta..sub.(min), and a
dash-dot line and frequency with subscript (max) for the maximum
period specified by angle .theta..sub.(max). The relatively narrow
range of periods can be overly restrictive for many applications.
An alternative interferometer design is depicted in FIG. 24b that
allows a much larger range of angles to be projected onto the
substrate. The design is identical to that described previously and
depicted in FIG. 24a, except that additional optic 270 has been
introduced. Optic 270, called an angular subtractor, expands the
range of angles in the interferometer. Two versions are described.
The first design, depicted in FIG. 24c, utilizes reflective optics.
Beams from AOM 79 are incident on angular subtractor 270a,
comprising mirrors 271 and prism 272. Left and right beams from AOM
79 reflect from mirrors 271 and prism 272, as shown, thus reducing
the angular spread between left and right beams. Beam-diameter
clipping at the apex of prism 272, for beams corresponding to
minimum angles of the AOM, limits the angular range of this method.
An alternative design, depicted in FIG. 24d, uses diffractive
optics to achieve a full range of angles. In this case, beams from
AOM 79 are incident on angular subtractor 270b, comprising lens
275, aperture plate 276, lens 277, grating 278, and aperture stop
279. The projection lens, comprising lens 275, aperture 276, and
lens 277, projects the image in AOM 79 onto transmission grating
278. Transmission grating 278 and stop 279 work in conjunction to
block zero and -1-order diffracted beams from left and right arms,
while allowing +1-orders to transmit. The function of grating 278
in FIG. 23d is identical to grating 278 in FIG. 23c. The
diffractive angular subtractor has the benefit that the full range
of angles may be overlapped, but with some loss of efficiency due
to the lost power in the zero and (-1) orders.
In the design depicted in FIG. 24a, an alternative AOD may be
readily defined which provides diffraction into multiple planes of
incidence. With reference to FIG. 24e, AOM 79 in FIG. 24a is
depicted as viewed along the -z direction. Sound wave 81a from left
transducer 80a travels counterposed to sound wave 81b from
transducer 80b. In FIG. 24f is depicted the same view of an
alternative AOD design which used four transducers 80 to produce
four counterposed sound waves 81. Light travelling in the
-z-direction is diffracted into multiple beams in two planes of
incidence crossed at 90 degrees. AO deflectors with even larger
numbers of opposed transducers may be defined, to provide multiple
planes of incidence. Extraneous diffracted beams may be blocked
using a cross or higher-order spatial filter aperture plate similar
to plate 72d in FIG. 19g, replacing spatial filter 72 in FIG. 24a.
Angular subtraction can be performed by generalizing the optical
device shown in FIG. 24c to have multiple sets of mirrors in
conjunction with a prism with multiple pairs of reflective faces,
where each opposed facet pair is dedicated to a particular plane of
incidence. An alternative means for angular subtraction is to
replace grating 278 in FIG. 24d with a multi-angled grating
beamsplitter. This multi-angled beamsplitter is composed of
multiple superimposed gratings each with a roll angle corresponding
to a particular beam pair, in a generalization of grating 278 shown
in FIG. 23c. Beam pairs reflecting from this grating appear to
diverge from a common point, similar to as depicted in FIG. 23c.
Apertures 279 or 72 block undesired higher-order beams.
The description of ways beams can be split and recombined to form
grating images on the substrate, and methods for electronic control
of grating period has been presented. Methods for real-time
measurement of image phase will now be provided. As discussed
previously and depicted in FIG. 7b, errors in the path of the x-y
stage during scanning will cause phase errors to be written into
the grating. In addition, disturbances in the optical components or
beam paths in the arms of the writing interferometer cause phase
shifts between the interferometer arms, corresponding to phase
errors in the image and thus in the written grating. Disturbances
common to optical systems include vibration, thermal expansion,
optical mount drift, and air turbulence. Several interferometer
designs, called phase reference interferometers, which measure the
image phase continuously in real time will now be described. When
used in conjunction with the writing interferometer and stage
interferometer, this information may be used to phase-lock the
writing interferometer to the substrate using means described
hereinafter.
The basic principles of the concept, illustrated for the case of a
single pair of beams in a single plane of incidence, are depicted
in FIG. 25. The writing interferometer, x-y stage, and stage
interferometer are similar to those described previously and
depicted in FIG. 2a. Components comprising the phase reference
interferometer (PRI) are mounted to rigid, stable optical block
175, which in turn is mounted to optical bench 20. The PRI is
mounted near the terminus of the left and right arms of the writing
interferometer at substrate 17 in order to minimize optical path
length errors to the substrate due to air turbulence. Small test
portions of left beam, with phase .phi..sub.L, and right beam, with
phase .phi..sub.R, are split by beamsplitters 171, and interfered
by beamsplitter 170 onto detectors 172. Signals from detectors 172
are analyzed by interferometer controller 35 to yield the phase
difference between the arms of the writing interferometer,
.DELTA..phi.=.phi..sub.L -.phi..sub.R.
The measured phase difference between the writing arms,
.DELTA..phi., can be used to phase lock the image to the stage, as
follows. Recall from earlier discussion that the relationship which
ensures phase locking of image to stage, for a constant-period,
non-rotating grating, is .DELTA..phi.=.DELTA..phi..sub.K
=2.pi.x.sub.S (t)/p+C, where .DELTA..phi..sub.K is the phase
difference between the arms during locking, x.sub.S (t) is the
stage x-velocity, and C is an arbitrary constant. Interferometer
controller 35 reports arm phase-difference .DELTA..phi. and stage
x-velocity x.sub.S (t) to controller 1. Controller 1 calculates
phase-lock error .delta..phi.=.DELTA..phi..sub.K -.DELTA..phi. and
attempts to control this signal to zero by applying a proportional
signal to piezoelectric controller 141, which in turn causes
piezoelectric actuator 140 to push on right-arm mirror 16b, thus
manipulating the phase of the right arm .phi..sub.R and thus
.DELTA..phi.. The control algorithm constitutes a feedback loop
controlling phase error .delta..phi. zero. Since mirror 16b can be
small and light, it can be moved quickly, thus rapidly nulling
error .delta..phi. associated with stage-path motion and writing
interferometer disturbances.
Referring again to FIG. 25, signals appearing on detectors 172 are
commonly in the form of sinusoidal voltages. These time-dependant
signals are analyzed to determine phase .phi.(t) and frequency
f(t). These quantities are related by the relations
f(t)=d.phi./dt/2.pi. and ##EQU7##
Using these relations, in the discussion that follows an expression
which relates frequencies is easily converted to an expression
relating phases, and vice versa.
In the following sections alternative and improved schemes for
detecting and manipulating image phase will be described, but first
a discussion of the limitations of common phase-control actuators
is necessary. With reference to FIG. 26a, a typical phase vs.
voltage curve is shown for light reflected from a
piezoelectrically-controlled (PZT) mirror, as depicted in FIG. 25,
or transmitted through a electro-optic phase modulator (EOM), which
will be described in more detail hereinafter. These types of
devices typically display phase shifts that are closely linear with
applied voltage, but with limits on the total phase excursion of
.+-..pi.N.sub..pi.. For example, N.sub..pi. is approximately 100
for a PZT mirror, whereas N.sub..pi. is approximately 2 for an EOM.
Note that while the PZT has a much larger phase range it has a much
slower response time: less than approximately 1 kHz for the PZT vs.
1 MHz for the EOM. Both these devices arc viable for scanning
schemes which require corrections for only small excursions of
phase error about .phi.=0, but careful attention must be paid to
centering the zero-phase point of the device around the expected
range of disturbances, and to the bandwidth and phase range
considerations.
Cross-scanning (Doppler) schemes, as depicted in FIG. 9, require
continuous, rapid, and unbounded changes of phase. The phase limit
of EOM and PZT devices can be circumvented by using a flyback
scheme, as follows. With reference to FIG. 26b, a phase function is
depicted which decreases with time in response to a nearly constant
stage x-velocity u.sub.S (t). At .phi.=.pi. boundaries, the voltage
is rapidly pulled from +V.sub..pi. to -V.sub..pi., which
corresponds to a phase change of 2.pi., and thus an invariant
phase. The device requires a finite flyback time, t.sub.FB, to
reset, which is longer for the PZT than the EOM. At slow scanning
speeds the flyback time is a small fraction of the time required to
scan from -.pi. to +.pi., with the effect that the flyback delay
introduces a negligible background dose to the grating image. At
faster scanning speeds the flyback time consumes a larger fraction
of the -.pi. to +.pi. scan time, and may lead to unacceptable
background doses. With reference to FIG. 26c, the frequency of the
phase device f=(1/2.pi.)d.phi./dt is depicted. Note the small time
intervals with positive frequency, corresponding to the flyback
time, where fringes are not locked.
An alternative method of effecting frequency shift is with an
acousto-optic modulator, described previously and depicted in FIG.
22c, which can provide a sustained frequency shift without
requiring flyback.
Now several alternative designs of phase reference interferometers
and means to measure writing-interferometer arms frequency
difference, and thus image fringe frequency, are described. In FIG.
27a are depicted the key components of a homodyne phase-reference
interferometer already described and depicted in FIG. 25. (While
this design is not strictly limited to measuring phase differences
between beams of the same frequency, it is distinguished from the
heterodyne technique, described below, where a separate
Doppler-shifted beam in mixed with the test beams.) Interference of
left and right test beams on detectors 172 yields the frequency
difference between the arms .DELTA.f=f.sub.L -f.sub.R. Depending of
the direction of scanning, frequency difference .DELTA.f may be
very small (e.g., during parallel scanning, as depicted in FIG. 5),
or large (e.g., during Doppler scanning, as depicted in FIG. 9).
For the case of .DELTA.f small, the well-known difficulties of
accurately measuring a slowly varying signal apply. For example,
any variations in beam intensity or detector efficiency may appear
to be fringe shifts and lead to errors.
These limitations may be avoided by using an improved heterodyne
phase-reference interferometer depicted in FIG. 27. The idea is to
mix light of frequency f.sub.H =f.sub.0 +F.sub.H with test portions
of both left and right beams, where f.sub.0 is the fundamental
light frequency as emitted by laser 11, typically 500-1000 THz, and
F.sub.H is a heterodyne frequency, typically 1-20 MHz. Since
electronic detectors cannot respond to the fundamental frequency
f.sub.0, only the difference frequencies are measured, effectively
modulating the information in the arms at the heterodyne frequency
that can be accurately measured using well known methods. The
heterodyne technique yields accurate frequency difference
measurements regardless of the stage scanning speed or method.
With reference to FIG. 27b, left and right beams from the writing
interferometer are intercepted by beamsplitters 171, which deflect
small test portions to beamcombiners 353. Optical fiber 350
delivers heterodyne beam of frequency f.sub.H, generated as
described below, to collimating lens 351, which creates a free
space beam. Beamsplitter 352 splits the heterodyne beam into left
and right beams. Left recombiner 353a mixes portion of left
writing-interferometer beam of frequency f.sub.L with left
heterodyne beam of frequency f.sub.H, yielding left heterodyne
difference frequency signal f.sub.LH =f.sub.L -f.sub.H on left
detector 173a. Similarly, right detector 173b measures right
heterodyne difference frequency signal f.sub.RH =f.sub.R -f.sub.H.
Controller 35 subtracts electronic signals f.sub.LH and f.sub.RH to
obtain the frequency difference between left and right arms
.DELTA.f=f.sub.L -f.sub.R =f.sub.LH -f.sub.RH.
With reference to FIG. 27c, a preferred method for generating the
heterodyne beam in fiber 350 is depicted. Beam from laser 11 of
frequency f.sub.0 impinges on acousto-optic modulator (AOM) 354.
The AOM is driven by controller 83 with RF frequency F.sub.H,
resulting in a zero-order beam of frequency f.sub.0 and diffracted
beam of frequency f.sub.H =f.sub.0 +F.sub.H. Lens 355 focuses the
diffracted beam onto fiber 350, which delivers signal to the
PRI.
An alternative PRI is depicted in FIG. 28, which avoids the need
for fiber optics and an external source of heterodyne light. In the
figure, s-polarized beams (E-vector normal to paper plane) are
indicated by a dot, and p-polarized beams (E-vector parallel to
paper plane) by a double-headed arrow. Left beam of frequency
f.sub.L is incident on half-wave plate 210, which rotates beam
polarization into 45-degree p and s portions. The beam then
impinges on AOM 211, driven by AOM controller 83 at RF frequency
F.sub.H. The AOM splits beam into zero-order beam of frequency
f.sub.L and diffracted beam of frequency f.sub.LH =f.sub.L
+F.sub.H. Specially cut birefringent prism 212 collimates beams
into s-polarized beam of frequency f.sub.LH =f.sub.L +F.sub.H, and
p-polarized beam of frequency f.sub.L. Aperture 215 blocks
extraneous s-polarized zero-order and p-polarized diffracted beams.
Beamsplitter 216 deflects test portion of beams which are then
mixed and interfered by 45-degree polarizer 217 onto detector 218,
which detects reference signal f.sub.ref =f.sub.LH -f.sub.L
=F.sub.H. Straight-through beam from beamsplitter 216 proceeds to
polarizing beamsplitter 220a, which allows p-polarized main beam to
travel straight through to substrate 17, while deflecting
s-polarized test beam to combiner 170. The p-polarized main beam is
converted to s-polarization by half-wave plate 221, impinging on
substrate 17. Meanwhile, s-polarized right beam of frequency
f.sub.R is split by beamsplitter 220b into main portion, which
proceeds to substrate 17 to overlap and interfere with left beam,
and test portion, which proceeds to combiner 170. The combiner
interferes left and right test beams on detectors 172, which
measured signal f.sub.pr =f.sub.LH -f.sub.R =.DELTA.f+F.sub.H.
Controller 35 subtracts signals f.sub.pr and f.sub.ref to obtain
.DELTA.f=f.sub.L -f.sub.R =f.sub.pr -f.sub.ref.
A PRI can also be used with writing interferometers employing an
objective lens, such as depicted in FIG. 23. With reference to FIG.
29a, a homodyne PRI is depicted. The writing interferometer is
identical to that in FIG. 23, except that pickoff beamsplitter 186
has been inserted in the objective lens to split small beam test
portions which impinge on mirror interferometer 185, described
previously and depicted in FIG. 22d. Mirror interferometer 185
causes left input beam of frequency f.sub.L(i) to interfere with
right input beam of frequency f.sub.R(i), and vice versa, creating
output beams of frequency difference .DELTA.f.sub.(i) =f.sub.L(i)
-f.sub.R(i). Output beams are imaged by objective lens, comprising
lenses 187 and 188, onto position-sensitive detector 230, such as a
linear diode array. Each position on the detector corresponds to a
different spatial frequency component in the image, allowing
simultaneous real-time measurement of the amplitude and relative
phase of each component.
With reference to FIG. 29b, an alternative homodyne PRI is
depicted. The writing interferometer is identical to that in FIG.
29a, except that mirror interferometer 185 has been removed. Test
beams split from main writing beams by beamsplitter 186 are imaged
onto imaging detector 230, such as a CCD array, by objective lens
187 and 188. Objective lens 187 and 188 forms a magnified virtual
image of image on substrate 17, which can then be analyzed to
determine image period, phase, and fringe rotation.
With reference to FIG. 30, a heterodyne PRI is depicted. The
writing interferometer is identical to that in FIG. 29, including
pickoff beamsplitter 186. Mixing beamsplitter 189 mixes test beams
from the writing interferometer with heterodyne beams from mirror
interferometer 185. Heterodyne beams are generated as follows.
Fiber 350 delivers heterodyne light of frequency f.sub.H to
collimating lens 351. Light reflects from scanning mirror 199,
which is rotated by actuator 140 under control of controller 141.
Two example paths through the optic are indicated, one by solid
line and one by dashed line. Each angle of deflection generates a
heterodyne probe beam to test a specific spatial-frequency
component in the writing image. Alternatively, an EOD or
multi-order grating beamsplitter can be used in place of scanning
mirror 199. An EOD would enable faster selection of spatial
frequencies to test. A grating beamsplitter would enable probing
multiple spatial frequencies simultaneously. Beam(s) from mirror
199 are collimated onto mirror interferometer 185 by lens 198.
Mirror interferometer 185 generates pair(s) of heterodyne beams for
testing the left and right components in the image. In the figure
only the beam pair indicated by the solid line corresponds to the
spatial frequency of the beams in the writing interferometer.
Beamsplitter 189 mixes the test beams from writing interferometer
with the heterodyne beams to generate beams with difference
frequencies f.sub.RH(i) =f.sub.R(i) -f.sub.H in the right arm, and
f.sub.LH(i) =f.sub.L(i) -f.sub.H for the left arm, which are imaged
by objective lens, comprising lenses 187 and 188, onto
position-sensitive detector 230, such as a linear diode array. Each
position on the detector corresponds to a different spatial
frequency component in the image, modulated by the heterodyne
frequency. By subtracting frequency signals corresponding to the
left and right components, the difference frequency for a specific
spatial frequency can be obtained from .DELTA.f.sub.(i)
=f.sub.LH(i) -f.sub.RH(i) =f.sub.L(i) -f.sub.R(i). Thus the
amplitude and phase of each spatial frequency component in the
image can be obtained.
A discussion of ways that the phase, frequency, and period of
spatial frequency components in the image can be obtained, and
demonstrated several means for controlling image phase has now been
provided. Several alternative and/or improved means of controlling
image phase and frequency will now be described. With reference to
FIG. 31, an improved method for controlling image phase over that
depicted in FIG. 8c is described. In FIG. 8c, actuator 140, such as
a piezoelectric actuator, is used to push mirror 16a, thus
shortening the length of the right arm and shifting its phase.
While electromechanical actuators generally have a large
.+-..pi.N.sub..pi. phase range, they are generally slow. On the
other hand, electro-optic modulator (EOM) phase shifters can shift
phase with megahertz bandwidth, but only over a narrow (<2.pi.)
phase range. In FIG. 31 both types are combined, which enables a
design with superior performance. Beam from laser 11 travels
through shutter/attenuator 12 and is split by beamsplitter 14 into
right and left arms. Mirrors 16 recombine and interfere beams onto
substrate 17. Right arm travels first through EOM phase shifter
143, and then reflects from mirror 16b, which is pushed by actuator
140. Master controller 1 sends signals to EOM controller 151 and
actuator controller 141 in order to provide the desired image
phase.
An alternative means of controlling image phase is depicted in FIG.
32. Beam from laser 11 reflects from mirror 13 and travels through
shutter/attenuator 12. Beam is split by grating 50 into zero and
.+-.m order diffracted beams. Zero-order beam is stopped by block
52 and diffracted beams are recombined and interfered on substrate
17 by mirrors 16. Actuator 140 pushes on grating 50 causing grating
to move distance .DELTA.x perpendicular to the incident beam. The
motion of the grating causes right beam to change phase by amount
.DELTA..phi..sub.Rm =-2.pi.m.DELTA.x/p, and the left beam to change
phase by amount .DELTA..phi..sub.Lm =2.pi.m.DELTA.x/p, where p is
the grating period. The phase shift of the image is thus
.DELTA..phi..sub.m =.DELTA..phi..sub.Lm -.DELTA..phi..sub.Rm
=4.pi.m.DELTA.x/p.
An alternative design in depicted in FIG. 33, which utilizes a
spinning circular grating rather than a linear one. The circular
range allows an unbounded range of phase shifting, or a sustained
Doppler shift by using continuous rotation. With reference to FIG.
33a, beam from laser 11 of frequency f.sub.0 travels through
shutter/attenuator 12, is turned by mirror 13, and diffracted by
circular grating 200. Detail of circular grating 200 is depicted in
FIG. 33b, showing grating region 201. Zero-order beam is stopped by
block 52 and diffracted beams are recombined and interfered on
substrate 17 by mirrors 16. Circular grating spins with angular
velocity .omega. producing right beam of frequency f.sub.R.omega.
=-2.pi.m.omega.r/g.sub..omega. and left beam of frequency
f.sub.L.omega. =2.pi.m.omega.r/g.sub.107 , where m is the
diffraction order, r is the radius of the grating, and
g.sub..omega. is the grating period. The image frequency is thus
.DELTA.f.sub..omega. =f.sub.L.omega. -f.sub.R.omega.
=4.pi.m.omega.r/g.sub.107 . Because of the difficulty of making
rapid velocity changes to the spinning grating, actuator 140 is
used to push mirror 16b in order to rapidly control small phase
errors between the arms. Alternatively an EOM phase modulator could
be used for even higher bandwidth.
An improved design for generating continuous frequency shifts
between the arms, which uses no moving parts, is depicted in FIG.
34. In this design, beam from laser 11 of frequency f.sub.0 travels
through shutter/attenuator 12 and is split into left and right arms
by beamsplitter 14. Beams are then diffracted by AO modulators 145
into zero-order beams blocked by stops 146, and diffracted beams,
which are directed to overlap and interfere at substrate 17 by
mirrors 16. AO controller 150 sends RF frequency F.sub.R to right
modulator and F.sub.L to left modulator, generating right beam of
frequency f.sub.R =f.sub.0 +F.sub.R and left beam of frequency
f.sub.L =f.sub.0 +F.sub.L, with frequency difference
.DELTA.f=f.sub.L -f.sub.R. While it is not strictly necessary to
use AO modulators in both arms, the use of counterposing modulators
ensures the left and right beams remain overlapped on substrate 17
even with large frequency shifts and thus large angular deflections
of the diffracted beams.
While the use of counterposing modulators ensures overlap of the
beams on substrate 17, independent of frequency shift, an
undesirable consequence is a tilt of the fringes out of the y-z
plane which will generate phase shifts due to substrate z-axis
motion or topography. An improved design that eliminates this
problem is depicted in FIG. 35. Beam from laser 11 of frequency
f.sub.0 travels through shutter/attenuator 12 and is split into
left and right arms by beamsplitter 14. Turning mirrors 24 send
beam through AO modulators 145. Zero-order beams are blocked by
stops 146, and diffracted beams are imaged by lenses 148 and 149
onto EO deflectors 10. AO controller 150 sends RF frequency F.sub.R
to right modulator and F.sub.L to left modulator, generating right
beam of frequency f.sub.R =f.sub.0 +F.sub.R and left beam of
frequency f.sub.L =f.sub.0 +F.sub.L, with frequency difference
.DELTA.f=f.sub.L -f.sub.R. Beams from AO modulators are deflected
in angle, as a function of frequency shift. However, EO deflectors
10 under control of controllers 151 correct the undesired angular
shifts. The frequency-shifted, angle-corrected beams are then
directed to overlap and interfere at substrate 17 by mirrors
16.
In FIGS. 23a and 23b were depicted means for generating grating
images using AO and EO deflectors and an objective lens recombiner.
Both these designs have limitations in Doppler scanning
applications. To review, in FIG. 23a an EO deflector was utilized,
so this design cannot be used for Doppler scanning, while the
design depicted in FIG. 23b utilizes a AO deflector, and so can be
used. However, at the short UV wavelengths of interest for
lithography, EO deflectors are generally capable of a much larger
angular range of deflection than AO deflectors, when expressed as a
ratio of the angular range divided by the angular divergence of the
beam (the so-called number of resolvable spots, see Yariv and Yey,
ibid., Chapter 10.2). The number of resolvable spots essentially
determines the number of distinct spatial frequency components in
the image that are available, and it is desirable to have this as
large as possible.
A design which combines elements of designs 23a and 23b is depicted
in FIG. 36, which enjoys both a large number of resolvable spots
and the capability of Doppler scanning. In this design beam from
laser 11 of frequency f.sub.0 travels through shutter/attenuator
12, is turned by mirror 13, and is split into left and right arms
by beamsplitter 5. Beams are frequency shifted by AO modulators 7.
Zero-order beams are blocked by stops 9, and diffracted beams are
turned by mirrors 6 and imaged onto EO deflectors 10 by lenses 148
and 149. AO modulators 7 provide Doppler shifting and multiple
angular beam generation over a small angular range, while EO
modulators 13 deflect this set of beams through a much larger
angular range. Beamsplitter 3 combines the left and right beams,
which are then imaged onto the wafer as described previously.
A description of ways that phase and frequency differences between
the interferometer arms can be measured and controlled has been
presented. In addition, undesired angular variations between the
arms can compromise the quality of the grating image and lead to
distortion and loss of contrast. Specifically, these are the angles
that the left and right beams make with respect to the substrate
surface. Eight degrees of freedom define the intersection of the
two beams on the substrate: left beam .theta..sub.L and .psi..sub.L
angles, left beam x.sub.L and y.sub.L lateral shift, right beam
.theta..sub.R and .psi..sub.R angles, and right beam x.sub.R and
y.sub.R lateral shift. These angles may vary due to vibration, air
turbulence, thermal expansion, or mounting drift of optical
components. FIG. 37 illustrates the consequences of phase and angle
errors in the interferometer arms. FIG. 37a depicts a grating
distorted by time-dependant phase shifts between the arms. The
stage moves from top to bottom, causing grating image to appear to
move from bottom to top of the substrate, writing grating stripe
361. At an early-time point image 361a has the desired phase. At a
mid-time point, however, writing interferometer drift causes the
phase of image 361b to shift a half-period to the right. At a
late-time point the phase of image 361c shifts back to the desired
position. The result is a grating stripe with an undesired
position-dependent phase error.
FIG. 37b depicts a distorted grating that would obtain due to
time-dependent 2.theta.-angle (in-plane) arm rotations between the
arms during scanning. The stage moves from bottom to top, writing
grating stripe 362. At an early time point image 362a moves along
the desired path with the desired period. At a mid-time point,
however, 2.theta. error causes the period of image 362b to
decrease. At a late-time point the period of image 362c returns to
the desired value. The result is a grating stripe with undesired
position-dependant period variations.
FIG. 37c depicts a distorted grating that would obtain due to
time-dependent .psi.-angle (out-of-plane) arm rotations during
scanning. The stage moves from bottom to top, writing grating
stripe 363. At an early time point image 363a moves along the
desired path with image rotation aligned with the direction of
motion. At a mid-time point, however, out-of-plane arm angular
errors cause image 363b to rotate clockwise. At a late-time point
image 363c has rotated back to the desired path. The result is a
grating stripe with undesired position-dependant linewidth
variations.
A variety of means may be employed to measure and correct for
interferometer arm angular errors. FIG. 38 depicts a couple of
direct homodyne methods for measuring beam angular errors. With
reference to FIG. 38a, right and left interferometer beams are
first split into main beams and weak first-test beams by
beamsplitters 370, which impinge onto two-axis position-sensitive
detectors 372. The main beam is split again by beamsplitters 371
into main beams and weak second-test beams that impinge on two-axis
position-sensitive detectors 373. The sixteen signals from the
position-sensitive detectors can be processed to extract the angles
and lateral shifts of the beams on substrate 17, using well-known
methods.
An alternative, more compact homodyne method is depicted in FIG.
38b. Right and left interferometer beams are split into main beams
and weak test beams by beamsplitters 375. Test beams are split into
lateral-shift test beams by beamsplitters 378, which impinge on
two-axis position-sensitive detectors 379, and angular-shift test
beams, which are focussed by lenses 376 onto two-axis
position-sensitive detectors 377. The sixteen signals from the
position-sensitive detectors can be processed to extract the angles
and lateral shifts of the beams on substrate 17, using well-known
methods.
An alternative homodyne method is depicted in FIG. 39 that utilizes
interference to measure beam angular variations. Right and left
interferometer beams are split into main beams and weak test beams
by beamsplitter 375. Test beams are split into lateral-shift test
beams by beamsplitters 378, which impinge on two-axis
position-sensitive detectors 379, and angular-shift test beams,
which are recombined and interfered by beamsplitter 380 onto
imaging detector 94. Interference fringes on imaging detector 94
are analyzed to directly extract the .theta. and .psi. angle
differences between the arms using well-known methods.
A heterodyne method can be utilized to measure beam angular
variations, as depicted in FIG. 40. Right and left interferometer
beams are split into main beams and weak test beams by
beamsplitters 375. Test beams are split into lateral-shift test
beams by beamsplitters 378, which impinge on two-axis
position-sensitive detectors 379, and angular shift test beams,
which proceed to the heterodyne interferometer. The heterodyne
interferometer comprises optical fiber 350 that delivers light of
frequency f.sub.H to lens 351, producing free-space beam impinging
on beamsplitter 352. Mixing beamsplitters 353 then combine and
interfere left and right heterodyne beams with left and right test
beams on quadrant detectors 381. The frequency of light measured at
detectors 377 is nominally f.sub.LH =f.sub.L -f.sub.H for the left
arm and f.sub.RH =f.sub.R -f.sub.H for the right arm, however,
small frequency shifts between different lateral sectors of each
beam are possible which indicate beam rotation. Each detector
quadrant yields a time-dependant signal that contains phase-shift
information modulated at the heterodyne frequency. Each quadrant
detector 381 can be used to determine beam angles .theta. and .psi.
for the arm by measuring the frequency difference between opposing
pairs of quadrants.
A description of ways that lateral and angular shifts between the
interferometer alms can be measured has been presented. Ways that
active optical components can be utilized to lock the beams on the
substrate using the measured information will now be provided.
Active optical components can also be used to compensate for stage
30 pitch and yaw errors that are known to stage x-y-.gamma.
controller. With reference to FIG. 41a, a method of steering beams
using actuated mirrors is depicted. Left and right beams reflect
from first two-axis actuated mirrors 410, which are pushed by
actuators 411 and 412, such as piezoelectric actuators, and then
reflect from second two-axis actuated mirrors 413, which are pushed
by actuators 414 and 415. Each mirror provides both .theta. and
.psi. tilts. The combination of two mirrors in each arm allows
correcting for all four beam lateral and angular degrees of freedom
per arm.
An alternative method utilizing electro-optic deflectors (EOD),
with,much higher bandwidth, is depicted in FIG. 41b. Left and right
beams pass through first .theta.-axis EODs 420, and then through
first .psi.-axis EODs 421, and then through second .theta.-axis
EODs 422, and then through second .psi.-axis EODs 423. The
combination of four EODs in each arm allows correcting for all four
beam lateral and angular degrees of freedom per arm.
A description of ways that errors due to writing interferometer arm
phase and frequency shifts, and arm lateral and angular variations,
can be measured and controlled has been presented. However, before
the writing interferometer can be usefully employed to inscribe
gratings on the substrate some means must be used to establish the
period, phase, and direction of the image fringes with respect to
the stage interferometer axes. Image period and phase must be
accurately measured in order to ensure that fringes in the image
remain locked to the substrate during stage motion. This is
accomplished by the use of special detectors and/or optics
traveling with the stage which serve as probes of the grating
image. This process is referred to as initiating phase lock between
the writing and stage interferometers. In practice, phase locking
is established at a set of locations outside of the substrate but
still on the substrate stage, and at times before and after an
episode of writing. During writing the position of the image
fringes with respect to the substrate is inferred from the
assumption of dimensional rigidity of the chuck and information
from the stage and phase reference interferometers. Phase drift
between the stage and writing interferometers is expected due to
thermal expansion and other disturbances, and needs to be
periodically rechecked. A stable thermal environment and the use of
phase-shift history reduces the frequency that phase locking needs
to be re-established.
The basic phase-locking concept is illustrated in FIG. 42. Detailed
descriptions of various alternative ways of phase locking are
described in FIGS. 43-52. With reference to FIG. 42, an
interferometer configuration similar to that depicted in FIG. 2a is
depicted, with some additional components. In FIG. 42a the
interferometer is first depicted as it would appear during writing
onto substrate 17. This configuration is called writing mode.
However, several critical alignments and measurements need to be
performed before writing can commence. In particular, the left and
right beams need to fully overlap on substrate 17 for high-contrast
fringes to be obtained, and the grating direction, period, and
phase need to be determined.
The first alignment step is to adjust the writing interferometer
such that the plane of incidence made by the left and right beams
is perpendicular to the x-y plane of motion of the substrate, and
that the bisector of the 2.theta. angle is also normal to this
plane. (It is assumed that substrate 17 has been adjusted to lie
parallel to the x-y plane.) This can be accomplished using
well-known optical methods. This alignment insures that the fringe
planes are perpendicular to the substrate surface. The next step is
to fully overlap the left and right beams on the substrate. FIG.
42b depicts the interferometer in a configuration where stage 30
has been moved such that two-axis position-sensitive detector 102,
such as a quadrant photodiode, is at the beam intersection, which
is useful for the purpose of establishing left and right beam
overlap.
The next alignment task is to ensure that the stage motion
direction during writing is accurately parallel to the fringes in
the grating image. Errors in determining stage motion parallelism
lead directly to a loss of contrast in the written grating, as
depicted in FIG. 7c. FIG. 42c depicts the interferometer in
reading-mode configuration, where stage 30 has been moved such that
reference beamsplitter 100 causes left and right beams to interfere
on imaging detectors 103. Beamsplitter 100 has been mounted such
that its face is accurately perpendicular to the x-y plane. The
face of beamsplitter 100 constitutes a reference surface to which
the direction of motion during scanning needs to be strictly
parallel. The first step of initiating phase locking is to
establish stage motion directions that are accurately parallel (x')
and perpendicular (y') to this face. Beamsplitter 100 is first
adjusted in angle until a flat interference fringe is obtained on
imaging detectors 103. Alternatively, the left and right beams may
be angle adjusted to achieve is the same result. This ensures that
the image fringe planes are parallel to the reference surface.
Stage 30 is started at position (x.sub.0,y.sub.0) and then moved a
distance .DELTA.y parallel to the y-axis. Since the y-axis is
unlikely to be perfectly parallel to the face of beamsplitter 100,
a sinusoidal signal is observed by detectors 103 while the stage is
moving, with a phase shift .DELTA..phi..sub.D
=(8.pi..DELTA.y/.lambda.) sin .theta. sin .epsilon., where .lambda.
is the laser wavelength, .theta. is the half-angle between the
interfering beams, and .epsilon. is the angle between the face of
beamsplitter 100 and the y-axis. This equation can be solved for
.epsilon., with an accuracy limited by the flatness of the
reference surface and the noise of the phase measurement
process.
The next task is to accurately determine the period and phase of
the fringes in the image using the stage interferometer as a
dimensional reference. Stage 30 is started at position
(x.sub.0,y.sub.0) and is then moved to position (.DELTA.x,.DELTA.x
sin .epsilon.) causing sinusoidal signals observed on detectors
103. The phase shift .DELTA..phi..sub.D of signal is then measured,
and the period of the image is then calculated from
p=2.pi..DELTA.x/.DELTA..phi..sub.D. The image phase zero is then
determined by noting a point x=x.sub..phi. where the signal crosses
zero voltage. (Because of the periodic nature of the fringes, the
phase zero point is indeterminate to an integer multiple of the
period, i.e., x.sub..phi..+-.np=x.sub..phi..
An alternative procedure for measuring image phase is depicted in
FIG. 42d. Here stage 30 has been moved to place test-grating 117
under the grating image. The test-grating period has been selected
such that first-order diffracted beams from left and right arms
overlap and interfere on imaging detector 124 with flat fringes.
Stage 30 is moved in the x-direction causing a sinusoidal signal to
be observed by detector 124. The phase of the signal accurately
determines the phase of the image, while the period of the signal
accurately measures the period of the grating.
At this point all information necessary to begin grating writing
has been obtained. The image period, phase, and angle, as measured
by the stage interferometer, are known, and can be re-measured
periodically if necessary to correct for optic shifts or thermal
drifts. In the following sections preferred methods for re-setting
phase lock between stage and writing interferometer are
described.
In the following sections, where FIGS. 43-52 are described, for
clarity only the substrate stage and phase-reference interferometer
(PRI) portions of the reading/writing interferometer are depicted
in the figures. For example, with regards to FIG. 25, these would
be the portions attached to substrate stage 30 and components
attached to PRI optical block 175.
With reference to FIG. 43, homodyne and in-line heterodyne methods
of detecting image phase using a stage beamsplitter are described.
In FIG. 43a the system is depicted in writing mode. The
phase-reference interferometer, comprising beamsplitters 171,
beammixer 170, and detectors 172, measures image frequency
.DELTA.f=f.sub.L -f.sub.R, which is used to maintain phase lock
between the writing interferometer and substrate 17, as described
previously.
In FIG. 43b a homodyne phase-locking system is depicted. The system
is depicted in reading mode, where stage 30 is moving in the +x
direction with velocity u.sub.S (t), which is known from the stage
interferometer electronics. Detectors 172 measure image frequency
.DELTA.f. The reading interferometer, comprising beamsplitter 100
and imaging detectors 103, measures stage frequency f.sub.S
=.DELTA.f-2f.sub.D +f.sub.E, where f.sub.D =(u.sub.S /.lambda.) sin
.theta.=u.sub.S /(2p) is the Doppler frequency and f.sub.E (t) is
the time-dependant frequency error between the phase reference and
reading interferometers, such as caused by thermal expansion.
Typically f.sub.E is very small (disturbances are slowly varying)
and can be ignored when measuring period if f.sub.D
>>f.sub.E, obtaining p=u.sub.S /(.DELTA.f-f.sub.S). The phase
error is obtained from ##EQU8##
where f.sub.E =f.sub.S -.DELTA.f+2f.sub.D and .phi..sub.E
=.phi..sub.0 at t=.sub.0.
Detectors 103 in FIGS. 43a-43c may be substituted for different
types of detectors, depending on details of the reading
interferometer design. When designed to be used in a homodyne mode,
the use of 2D imaging detectors for detectors 103 allows direct
imaging of fringes, and thus allows direct measurement of changes
of .theta. and .psi. angles between the arms. This is especially
useful during initial alignment. However, when the reading
interferometer is designed to be used in heterodyne mode, fringes
on detectors 103 will typically be moving too rapidly to be
accurately imaged. In this case, heterodyne quadrant detector
schemes, discussed earlier and depicted in FIG. 40, are more
useful.
With reference to FIG. 43c, an in-line heterodyne phase locking
scheme is depicted. In this embodiment the optical configuration is
identical to that depicted in FIG. 43b, except that the left arm
has been up-shifted by frequency f.sub.H /2 and the right arm has
been down-shifted by frequency f.sub.H /2. These frequency shifts
could be affected by designs depicted in FIGS. 34-36. Detectors 172
measure heterodyne image frequency .DELTA.f.sub.H
=.DELTA.f+f.sub.H, while detectors 103 measure stage frequency
f.sub.SH =.DELTA.f.sub.H -2f.sub.D +f.sub.E. The method for
measuring the image period and phase error is identical to that
described previously and depicted in FIGS. 43a and 43b. Here the
period of the image is obtained from p=u.sub.S /(.DELTA.f.sub.H
-f.sub.SH) and the frequency error from f.sub.E =f.sub.SH
-.DELTA.f.sub.H +2f.sub.D. The advantage of heterodyne frequency
shifting the signals, measured by the phase reference and reading
interferometers, is the immunity to low-frequency noise. The
in-line heterodyne technique can be used with all other types of
stage beam combiners, such as pinholes, optical fibers, gratings,
or prisms, as described hereinafter.
The heterodyne phase-reference interferometer described previously
and depicted in FIG. 27b needs to be modified slightly in design
and usage when used in conjunction with in-line heterodyne phase
locking. In FIG. 44a the interferometer is depicted in writing
mode. Left and right arms are split by beamsplitters 171 into weak
test beams and main beams that impinge and interfere on substrate
17. Test beams proceed to the mixing interferometer comprising
optical fiber 350 delivering heterodyne light of frequency f.sub.H,
collimating lens 351, beamsplitter 352, and mixing beamsplitter
cubes 353. An AO modulator, as depicted in FIG. 27c could generate
heterodyne light. Beamsplitters 353 mix heterodyne beams with test
beams on detectors 173, generating signal f.sub.LH =f.sub.L
-f.sub.H in left detector 173a, and signal f.sub.RH =f.sub.R
-f.sub.H in right detector 173b. The image frequency is calculated
from .DELTA.f=f.sub.L -f.sub.R =f.sub.LH -f.sub.RH.
In FIG. 44b the interferometer is depicted in reading mode. In this
case heterodyne light in fiber 350 is turned off, and the
interferometer functions identically to the in-line heterodyne
interferometer depicted in FIG. 43c and described previously, and
the image period and frequency error are calculated as
described.
Now a method is described of phase-locking writing and stage
interferometers utilizing a heterodyne interferometer on the stage.
This method has the advantage that the phase reference signal needs
never to be interrupted, and that no in-line frequency shifting in
the arms is required. With reference to FIG. 45a, the
interferometer is depicted in writing mode. The design features a
heterodyne phase-reference interferometer identical to that
depicted in FIG. 27b and described previously. However, in this
design, heterodyne light in fiber 350 is split off with fiber
beamsplitter 357 into fiber spur 358 that travels to a reading
interferometer attached to stage 30, comprising lens 323,
beamsplitters 322, mixers 320, and detectors 321. During the time
that the interferometer is configured in writing mode, as shown in
FIG. 45a, no signal is measured by the reading interferometer.
FIG. 45b depicts the interferometer in reading mode. In this case
the stage has been moved such that the beams no longer intersect at
substrate 17, but rather impinge on the heterodyne reading
interferometer. The left beam of frequency f.sub.L and right beam
of frequency f.sub.R are allowed to cross and impinge on
beamsplitters 320, which mix the beams from the reading arms with
heterodyne light of frequency f.sub.H, which are then measured by
detectors 321. Heterodyne light is provided by spur fiber 358
described previously, which delivers light of frequency f.sub.H
onto collimating lens 323. Beam from lens 323 is then split into
two beams by beamsplitter 322 that travel to mixing beamsplitters
320, as described previously. At all times the phase reference
interferometer provides image frequency .DELTA.f=f.sub.L -f.sub.R
=f.sub.LH -f.sub.RH, where f.sub.LH -f.sub.L -f.sub.H is measured
by left phase reference detector 171a and f.sub.RH =f.sub.R
-f.sub.H is measured by right phase reference detector 171b. During
image measurement the left-arm detector 321b measures signal
f.sub.SLH =f.sub.LH -f.sub.D +f.sub.EL and the right-arm detector
321a measures signal f.sub.SRH =f.sub.RH +f.sub.D +f.sub.ER, where
f.sub.D =(u.sub.S /.lambda.) sin .theta.=u.sub.S /(2p) is the
Doppler frequency for stage velocity u.sub.S, and f.sub.EL and
f.sub.ER are the left and right arm frequency errors, respectively.
The stage frequency is calculated from f.sub.S =f.sub.SLH
-f.sub.SRH =.DELTA.f-2f.sub.D +f.sub.E, where f.sub.E =f.sub.EL
-f.sub.ER. The period of the image is obtained from p=u.sub.S
/(.DELTA.f-f.sub.S) and the frequency error from f.sub.E =f.sub.S
-.DELTA.f+2f.sub.D.
Alternatively to the use of a beamsplitter 100 attached to stage
30, as shown previously in FIG. 42, a number of other means of
measuring image period and phase in reading mode are possible, as
depicted in FIG. 46. The cases depicted in FIG. 46 show only the
region near the overlap of the reading/writing interferometer arms.
In all cases the depicted objects are attached to stage 30.
Fringe-detection schemes depicted in FIGS. 46(a-c,e) use
beamsplitters, lenses and other optical components, which may
possibly introduce phase errors into the measurement due to the
figure quality of the optics. Detection schemes depicted in FIGS.
46(d,f-h) have the advantage that they directly image individual
fringes, introducing minimal phase measurement error, although at
the expense of reduced signal.
FIG. 46a depicts cube beamsplitter 101 that interferes left and
right beams onto detectors 103. The advantage of cube beamsplitter
101 over flat beamsplitter 100 used in FIG. 42 is the larger range
of accessible angles and better immunity to thermal fluctuations.
For large periods, corresponding to small 2.theta. angles, beam
occlusion prevents the use of beamsplitters. FIG. 46b depicts the
use of mirrors 106 to open the beam-crossing angle, thus decreasing
beam occlusion. FIG. 46c depicts an alternative method of
decreasing beam occlusion by using lenses 109 and 110.
FIG. 46d depicts a detector 124 that is able to detect individual
fringes in the image. FIG. 46e depicts lens 109 that magnifies
fringes in the image such that individual fringes can more easily
be detected by detector 124. FIG. 46f depicts an aperture 107 that
is sufficiently small to allow individual fringes to be observed by
detector 125. FIG. 46g depicts an aperture 107 that is sufficiently
small to allow individual fringes to be picked up by fiber 108 and
delivered to detector 125. FIG. 46h depicts a small asperity 105 on
the surface of plate 110 which is sufficiently small to allow
individual fringes to be scattered onto detector 125. In FIGS.
46(f-h), larger signals could be obtained by using a lens to
collect and focus light from the aperture or asperity.
Many alternative means for measuring image period and phase can be
described that use is reflective prisms or corner cubes attached to
stage 30. The most useful are depicted in FIGS. 47 and 48. In the
figures, prism 1118 is attached to stage 30, and travels with
velocity us, while all other components are attached to optical
bench 20 (see FIG. 42). In many of the following FIGS. 47-52, the
optical components and beams comprising the phase reference
interferometer have been suppressed for clarity.
With reference to FIG. 47a, incident left and right reading beams
are split by beamsplitters 99 into reference beams that proceed to
beamsplitters 93, and test beams that proceed to prism 118. Test
beams reflect from prism 118 onto beamsplitters 93, are mixed with
reference beams, and measured by detectors 103. Detectors 103
measure signal f.sub.SI =f.sub.DP +f.sub.E, where Doppler frequency
f.sub.DP =(u.sub.S /.lambda.)(sin .theta.+sin .beta.), f.sub.E is
the error frequency, u.sub.S is the stage velocity, .theta. is the
azimuthal angle and .beta. is the angle between the reflected beams
and the stage normal. The period of the image is obtained from
p=(1/2)/(f.sub.DP /u.sub.S +sin .beta./.lambda.) and the frequency
error from f.sub.E =f.sub.SI -f.sub.DP. A disadvantage of all
methods depicted in FIG. 47 is that an accurate determination of p
and f.sub.E requires an accurate determination of angle .beta..
FIG. 47b depicts a configuration similar to FIG. 47a, except that
prism 118 has been designed such that .beta.=.theta.. In this case,
incident left and right reading beams are split by beamsplitters 99
into reference beams, which reflect from mirrors 111 back to
detectors 103, and test beams that proceed to prism 118. Test beams
reflect from prism 118 back to beamsplitters 111, and are mixed
with reference beams onto detectors 103, measuring signal f.sub.SI
=f.sub.DP +f.sub.E where f.sub.DP =2 sin .theta.u.sub.S /.lambda..
The period of the image is obtained from p=u.sub.S /f.sub.DR and
the frequency error from f.sub.E =f.sub.SI -f.sub.DP.
An alternative configuration that mixes left and right
Doppler-shifted beams is depicted in FIG. 47c. Here incident left
and right reading beams reflect from prism 118 and are directed by
mirrors 106 onto beamsplitter 101, which mixes left and right beams
onto detectors 103, measuring signal f.sub.SR =.DELTA.f-2f.sub.DP
+f.sub.E. The period of the image is obtained from
p=(1/2)/(f.sub.DP /u.sub.S +sin .beta./.lambda.) and the frequency
error from f.sub.E =f.sub.SR -.DELTA.f+2f.sub.DP.
FIG. 47d depicts a configuration similar to FIG. 47c, except that
prism 118 has been designed such that .beta.=.theta.. Here incident
left and right reading beams transmit through beamsplitters 99 and
reflect from prism 118 back to beamsplitters 99, which direct them
to beamsplitter 101, mixing left and right beams onto detectors
103, measuring signal f.sub.SR =.DELTA.f-2f.sub.DP +f.sub.E. The
period and frequency errors are determined identically as the
method depicted in FIG. 47c.
FIG. 48 depicts heterodyne methods of measuring image period and
phase using a chuck prism. With reference to FIG. 48a, incident
left and right reading beams are reflected by prism 118, attached
to stage 30, becoming test beams that transmit through beam mixers
99 to detectors 103. Heterodyne light of frequency f.sub.H is
brought through fiber 350 and collimated by lens 351 into
free-space beam that is split by beamsplitter 101 into left and
right reference beams. Reference beams are mixed with test beams by
mixers 99 onto detectors 103. Left detector 103a measures signal
f.sub.LHD =f.sub.L -f.sub.DP -f.sub.H +f.sub.EL and right detector
99b measures signal f.sub.RHD =f.sub.R +f.sub.DP -f.sub.H
+f.sub.ER. The difference frequency is calculated from f.sub.SR
=f.sub.LHD -f.sub.RHD =.DELTA.f-2f.sub.DP +f.sub.E, where f.sub.DP
=(u.sub.S /.lambda.)(sin .theta.+sin .beta.). The period of the
image is obtained from p=(1/2)/(f.sub.DP /u.sub.S +sin
.beta./.lambda.) and the frequency error from f.sub.E =f.sub.EL
-f.sub.ER =f.sub.SR -.DELTA.f+2f.sub.DP.
FIG. 48b depicts a configuration similar to FIG. 48a, except that
prism 118 has been designed such that .beta.=.theta.. Here incident
left and right reading beams transmit through beamsplitters 99 and
reflect from prism 118 back to beamsplitters 99, which reflect
beams to mixers 93. Heterodyne light of frequency f.sub.H is
brought through fiber 350 and collimated by lens 351 into
free-space beam that is split by beamsplitter 101 into left and
right reference beams. Reference beams are mixed with test beams by
mixers 93 onto detectors 103. The period and frequency errors are
determined identically as the method depicted in FIG. 48a.
Many alternative means for measuring image phase can be described
that utilize gratings attached to stage 30. Both reflection and
transmission grating designs can be described. The most useful
reflection grating designs are depicted in FIGS. 49 and 50. In the
figures, grating 117 is attached to stage 30, and travels with
velocity u.sub.S, while all other components are attached to
optical bench 20 (see FIG. 42), although alternative designs can be
described where the these components are attached to, and travel
with, stage 30.
With reference to FIG. 49a, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the same arm
reflected from the grating. In the figure only beams generated by
the right arm of the writing interferometer are depicted. Light
from right arm impinges on grating 117 and splits into reflected
zero-order and diffracted nth-order beams. Zero-order beam reflects
from splitter 99a and transmits through mixer 93a, forming
reference beam of frequency f.sub.R. The nth-order diffracted beam
from substrate 117 reflects from mixer 93a, forming test beam of
frequency f.sub.Rn =f.sub.R +f.sub.Dn +f.sub.E. Test and reference
beams interfere and are measured by detector 103a, generating
signal f.sub.Sn1 =f.sub.Dn +f.sub.E, where f.sub.Dn =nu.sub.S /g
and g is the grating period. The frequency error is obtained from
f.sub.E =f.sub.Sn1 -f.sub.Dn.
With reference to FIG. 49b, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm. In
the figure only beams generated by the right arm of the writing
interferometer are depicted. Light from right arm impinges on
grating 117 and splits into reflected zero-order and diffracted
nth-order beams. The nth-order beam reflects from mixer 93a,
forming test beam of frequency f.sub.Rn. Left beam reflects from
splitter 99a and transmits through mixer 93a, forming reference
beam of frequency f.sub.L. Test and reference beams interfere and
are measured by detector 103a, generating signal f.sub.Sn2
=.DELTA.f-f.sub.Dn +f.sub.E. The frequency error is obtained from
f.sub.E =f.sub.S2n +f.sub.Dn -.DELTA.f.
With reference to FIG. 49c, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
diffracted by the grating. Light from left arm impinges on grating
117 and splits into reflected zero-order and diffracted mth-order
beams of frequency f.sub.L2m -f.sub.L -f.sub.Dm +f.sub.EL.
Diffracted beam reflects from mirror 106b through mixer 99 onto
detectors 103. Meanwhile, light from right arm impinges on grating
117 and splits into reflected zero-order and diffracted nth-order
beams of frequency f.sub.R2n =f.sub.R +f.sub.Dn +f.sub.ER.
Diffracted beam reflects from mirror 106a through mixer 99 onto
detectors 103. Detectors 103 measure signal f.sub.S3nm
=.DELTA.f+f.sub.Dn +f.sub.Dm +f.sub.E. The frequency error is
obtained from f.sub.E =f.sub.EL -f.sub.ER =f.sub.S3nm +f.sub.Dn
+f.sub.Dn -.DELTA.f.
With reference to FIG. 49d, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
diffracted by the grating, where the diffracted beams are
coincident. Light from left arm impinges on grating 117 and splits
into reflected zero-order and diffracted mth-order beams, while
light from right arm impinges on grating 117 and also splits into
reflected zero-order and diffracted nth-order beams, where the
diffracted beams are coincident in angle. Diffracted beams impinge
on detector 124, which measures signal f.sub.S3nm. The frequency
error is obtained from f.sub.E =f.sub.EL -f.sub.ER =f.sub.S3nm
+f.sub.Dn +f.sub.Dm -.DELTA.f.
With, reference to FIG. 49e, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the same arm. In the
figure only beams generated by the left arm of the writing
interferometer are depicted. Light from left arm is split by
beamsplitter 99a into reference and test beams. Test beam impinges
on substrate 117 and is nth-order diffracted, acquiring frequency
f.sub.Ln, and is reflected by beamsplitter 93a to detector 103a.
Reference beam transmits through beamsplitter 93a, mixing and
interfering with test beam. Detector 103a measures signal f.sub.S1n
=f.sub.Dn +f.sub.E. The frequency error is obtained from f.sub.E
=f.sub.Sn1 -f.sub.Dn.
With reference to FIG. 49f, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
reflected by the grating. In the figure only beams generated by the
left arm of the writing interferometer are depicted. Light from
left arm transmits through beamsplitter 99a, diffracts from
substrate 117, now acquiring frequency f.sub.Ln, and reflects from
beamsplitter 93a onto detector 103a. Light from right arm reflects
from substrate 117, reflects from beamsplitter 99a, and transmits
through beamsplitter 93a onto detector 103a. Detector 103a measures
signal f.sub.S2n. The frequency error is obtained from f.sub.E
=f.sub.S2n +f.sub.Dn -.DELTA.f.
With reference to FIG. 49g, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
reflected by the grating, where the incident, diffracted, and
reflected beams are coincident. Beams from reading arms transmit
through beamsplitters 99 and are split into reflected and
diffracted beams by substrate 117. Reflected beams are directed by
opposite beamsplitters 99 to detectors 103, while diffracted beams
are reflected by same-side beamsplitters 99 to detectors 103.
Detectors 103 measure signal f.sub.S2n. The frequency error is
obtained from f.sub.E =f.sub.S2n +f.sub.Dn -.DELTA.f.
With reference to FIG. 49h, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
reflected by the grating, where the diffracted and reflected beams
are coincident, and cast into a different plane than the incident
beams by tilting the plane of incidence. Light from reading arms is
split into reflected and diffracted beams by substrate 117.
Diffracted beams from each arm interfere with reflected beams from
opposite arm onto detectors 103, measuring signal f.sub.S2n. The
frequency error is obtained from f.sub.E =f.sub.S2n +f.sub.Dn
-.DELTA.f.
FIG. 50 depicts a heterodyne method of measuring image phase using
a reflection grating. Incident left and right writing beams are
diffracted by grating 117, attached to stage 30, becoming test
beams that reflect from beam mixers 99 to detectors 103. Heterodyne
light of frequency f.sub.H is delivered by fiber 350 and collimated
by lens 351 into free-space beam that is split by beamsplitter 101
into left and right reference beams. Reference beams are mixed with
test beams by mixers 99 onto detectors 103. Left detector 103a
measures signal f.sub.LHGn =f.sub.L -f.sub.Dn -f.sub.H +f.sub.EL
and right detector 99b measures signal f.sub.RHGm =f.sub.R
+f.sub.Dm -f.sub.H +f.sub.ER. The stage frequency is calculated
f.sub.SGmn =f.sub.LHGn -f.sub.RHGm =.DELTA.f-f.sub.Dn -f.sub.Dm
+f.sub.E. The frequency error is obtained from f.sub.E =f.sub.EL
-f.sub.ER =f.sub.SGmn +f.sub.Dn +f.sub.Dm -.DELTA.f.
Many alternative means for measuring image phase can be described
that utilize transmission gratings attached to stage 30. The most
useful are depicted in FIGS. 51 and 52. In the figures, grating 117
and all other optical components shown are attached to stage 30,
and travel with velocity u.sub.S, although alternative designs can
be described where the these components are attached to optical
bench 20 (see FIG. 42).
With reference to FIG. 51a, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm transmitted by the grating with light from the opposite arm
diffracted from the grating, such that the zero order of each arm
is coincident with a diffracted order of the opposite arm. Light
from each arm is split by grating 117 into zero-order hand
diffracted beams, which impinge on detectors 103. Light from
opposite arms interfere and are measured by detectors 103,
generating signal f.sub.S =.DELTA.f-2f.sub.D +f.sub.E. The
frequency error is obtained from f.sub.E =f.sub.S
-.DELTA.f+2f.sub.D.
With reference to FIG. 51b, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
diffracted by the grating, such that diffracted beams are
coincident. Light from each arm is split by grating 117 into
zero-order (not shown) and diffracted beams, which impinge on
detector 124. Coincident diffracted light from opposite arms
interfere and are measured by detectors 103, generating signal
f.sub.S. The frequency error is obtained from f.sub.E =f.sub.S
-.DELTA.f+2f.sub.D.
With reference to FIG. 51c, an interferometer configuration is
depicted which measures image phase by interfering light from each
arm diffracted by the grating with light from the opposite arm
diffracted by the grating, such that diffracted beams are not
coincident. Light from each arm is split by grating 117 into
zero-order (not shown) and diffracted beams, which are directed by
mirrors 106 to beamsplitter 101, which in turn overlaps and
interferes the diffracted beams from both arms onto detectors 103,
generating signal f.sub.S. The frequency error is obtained from
f.sub.E =f.sub.S -.DELTA.f+2f.sub.D.
FIG. 52 depicts a heterodyne method of measuring image phase using
a transmission grating. Incident left and right reading beams are
diffracted by grating 117, attached to stage 30, becoming test
beams that reflect from beam mixers 99 to detectors 103. The left
beam of initial frequency f.sub.L is Doppler shifted to frequency
f.sub.L -f.sub.D +f.sub.EL, and the right beam of initial frequency
f.sub.R is Doppler shifted to frequency f.sub.R +f.sub.D +f.sub.ER.
Heterodyne light of frequency f.sub.H is delivered by fiber 350 and
collimated by lens 351 into free-space beam that is split by
beamsplitter 101 into left and right reference beams. Reference
beams are mixed with test beams by mixers 99 onto detectors 103.
Left detector 103a measures signal f.sub.SLH =f.sub.L -f.sub.D
-f.sub.H +f.sub.EL and right detector 99b measures signal f.sub.SRH
=f.sub.R +f.sub.D -f.sub.H +f.sub.ER. The difference frequency is
calculated from f.sub.S =f.sub.SLH -f.sub.SRH =.DELTA.f-2f.sub.D
+f.sub.E. The frequency error is obtained from f.sub.E =f.sub.EL
-f.sub.ER =f.sub.S.DELTA.f+2f.sub.D.
The following is a glossary of terms for use with the description
of the invention:
IL interference lithography, also known as interferometric
lithography or holographic lithography SBIL scanning beam
interference lithography AIL achromatic interference lithography RF
radio frequency UV ultraviolet writing interferometer
interferometer configured to write fringes on substrate reading
interferometer interferometer configured to read periodic patterns
on substrate phase-reference interferometer (PRI) subsystem of
writing/reading interferometer designed to measure phase or
frequency difference between the arms homodyne PRI PRI where the
arms are mixed with each other heterodyne PRI PRI where each arm is
mixed with a heterodyne beam plane of incidence (POI) plane made by
left and right interferometer arms incident on substrate image
periodic pattern on substrate resulting from intersection of
writing interferometer beams image plane plane of substrate surface
image phase phase difference between left and right interferometer
arms image frequency frequency difference between left and right
interferometer arms angular heterodyne optic which expands a small
range of angles about a large angle offset into a range of angles
about zero angle .theta. half the angle between the arms of
reading/writing interferometer, also called the half angle or
azimuthal angle .psi. rotation angle of the POI about the z axis,
defined as the CCW angle between the x axis and the intersection of
the POI with the x-y plane, corresponding to the rotation of
fringes in the x-y plane, defined as the CCW angle between the y
axis and the image fringes .zeta. tilt angle of POI from the z axis
.lambda. wavelength of light in beams f = c/.lambda. frequency of
light in beams c speed of light p = .lambda./(2sin.theta.) grating
period of image p.sub.1, p.sub.2, p.sub.3, . . . period in first,
second, third, etc . . . , scans .DELTA.p period difference between
adjacent scans q = 1/p grating spatial frequency x x-coordinate of
stage reference frame y y-coordinate of stage reference frame z
z-coordinate of stage reference frame (grating image is fixed in
stage frame at x = y = z = 0) t time x.sub.S (t) x-position of
substrate center in stage frame y.sub.S (t) y-position of substrate
center in stage frame z.sub.S (t) z-position of substrate surface
at image center (stage frame x = y = 0) u.sub.S (t) = dx.sub.S /dt
x-axis velocity of substrate in stage frame v.sub.S (t) = dy.sub.S
/dt y-axis velocity of substrate in stage frame w.sub.S (t) =
dz.sub.S /dt z-axis velocity of substrate surface at image center
(stage frame x = y = 0) x.sub.L (t) x-position of left beam center
in stage frame y.sub.L (t) y-position of left beam center in stage
frame x.sub.R (t) x-position of right beam center in stage frame
y.sub.R (t) y-position of right beam center in stage frame
.theta..sub.(i) angle between beams in writing/reading
interferometer for ith pair of beams in single plane of incidence N
number of beam pairs i = 1, 2, 3, . . . , N index for N beam pairs
d beam diameter d.sub.par = d/cos.theta. image diameter on
substrate in direction parallel to plane of incidence d.sub.perp =
d image diameter on substrate in direction perpendicular to plane
of incidence .DELTA.x = Mp << d.sub.par stage scanning
increment, equals integer multiple M of period p M integer period
increment x.sub.0 desired stage x-axis position during scanning
.delta.x.sub.S (t) = x.sub.S (t) - x.sub.0 << p x-axis
position error during scanning and condition for controlling stage
lateral error .delta..phi.(t) = 2.pi..delta.x.sub.S /p <<
2.pi. grating phase error during scanning and condition for
controlling grating phase error .gamma..sub.0 desired stage yaw
during scanning .delta..gamma..sub.S (t) = .gamma..sub.S (t) -
.gamma..sub.0 << p/d stage yaw error during scanning and
condition for controlling stage yaw error L.about.p/2 width of
grating lines in image .delta.L(t) = d.delta..gamma..sub.S (t)
<< L linewidth variation during scanning and condition for
controlling stage yaw error .phi..sub.L phase of left
writing-interferometer arm .phi..sub.R phase of right
writing-interferometer arm .DELTA..phi. = .phi..sub.L - .phi..sub.R
phase difference between left and right interferometer arms, also
known as image phase f.sub.L = d.phi..sub.L /dt/2.pi. frequency of
left writing-interferometer arm f.sub.R = d.phi..sub.R /dt/2.pi.
frequency of right writing-interferometer arm .DELTA.f = f.sub.L -
f.sub.R = d.DELTA..phi./dt/2.pi. frequency difference between left
and right interferometer arms, also known as image frequency
x.sub.F (t) = p.DELTA..phi./2.pi. fringe x-position u.sub.F =
dx.sub.F /dt = p.DELTA.f fringe x-velocity x.sub.F (t) = x.sub.S
(t) condition for stage x-position phase locking u.sub.F (t) =
u.sub.S (t) condition for stage x-velocity frequency locking
.DELTA..phi..sub.K = 2.pi.x.sub.S (t)/p + C locked image phase
necessary to lock image to stage .delta..phi. = .DELTA..phi..sub.K
- .DELTA..phi. image phase-lock error controlled to zero
.DELTA.f.sub.K = d.DELTA..phi..sub.K /dt/2.pi. = u.sub.S (t)/p
locked image frequency necessary to lock image to stage C arbitrary
phase constant X X-coordinate of substrate reference frame Y
Y-coordinate of substrate reference frame Z Z-coordinate of
substrate reference frame R = (X.sup.2 + Y.sup.2).sup.1/2 radius
coordinate of substrate reference plane .gamma. substrate rotation
(yaw) .gamma..sub.S (t) substrate rotation (yaw) CW angle between
X-Y and x-y axes .omega..sub.S (t) = d.gamma..sub.S /dt substrate
rotational velocity (spin) Z.sub.W (X,Y) map of image surface
height X.sub.B (t) = -x.sub.S cos.gamma..sub.S + y.sub.S
sin.gamma..sub.S X position of image center in substrate frame
Y.sub.B (t) = -x.sub.S sin.gamma..sub.S - y.sub.S cos.gamma..sub.S
Y position of image center in substrate frame Z.sub.B (t) = Z.sub.W
(X.sub.B, Y.sub.B) = z.sub.S (t) Z position of substrate surface at
image center U.sub.B (t) = dX.sub.B /dt = (x.sub.S.omega..sub.S +
v.sub.S)sin.gamma..sub.S + (y.sub.S.omega..sub.S -
u.sub.S)cos.gamma..sub.S X velocity of image center in substrate
frame V.sub.B (t) = dY.sub.B /dt = (y.sub.S.omega..sub.S -
u.sub.S)sin.gamma..sub.S - (x.sub.S.omega..sub.S +
v.sub.S)cos.gamma..sub.S Y velocity of image center in substrate
frame ##EQU9## Z velocity of substrate surface at image center K
number of planes of incidence j = 1, 2, 3, . . . , K index for K
planes of incidence N.sub.j number of beam pairs in plane of
incidence (POI)j N number of beam pairs for case K = 1 i = 1, 2, 3,
. . . , N.sub.j index for N.sub.j beam pairs (i, j) indicates ith
beam pair in jth plane of incidence (i) indicates ith beam pair in
single plane of incidence (K = 1) (min) beam pair corresponding to
minimum .theta. angle (largest spatial frequency) (max) beam pair
corresponding to maximum .theta. angle (smallest spatial frequency)
a.sub.L(i,j) amplitude of left beam of ith beam pair in POIj
.phi..sub.L(i,j) phase of left beam of ith beam pair in POIj
f.sub.L(i,j) = d.phi..sub.L(i,j) /dt/2.pi. frequency of left beam
of ith beam pair in POIj .theta..sub.L(i,j) azimuthal angle of left
beam of ith beam pair in POIj .psi..sub.L(i,j) rotation angle of
left beam of ith beam pair in POIj a.sub.R(i,j) amplitude of right
beam of ith beam pair in POIj .phi..sub.R(i,j) phase of rigbt beam
of ith beam pair in POIj f.sub.R(i,j) = d.phi..sub.R(i,j) /dt/2.pi.
frequency of right beam of ith beam pair in POIj .theta..sub.R(i,j)
azimuthal angle of right beam of ith beam pair in POIj
.psi..sub.R(i,j) rotation angle of right beam of ith beam pair in
POIj a.sub.(i,j) = a.sub.L(i,j) + a.sub.R(i,j) = 2a.sub.L(i,j) =
2a.sub.R(i,j) image amplitude .psi..sub.j = (.psi..sub.L(i,j) +
.psi..sub.R(i,j))/2 rotation angle of POIj (constant) .zeta..sub.j
= (.psi..sub.L(i,j) - .psi..sub.R(i,j))/2 tilt of POIj
(constant) .delta..psi..sub.L(i,j) rotation angle error of left
beam out of POI .delta..psi..sub.R(i,j) rotation angle error of
right beam out of POI .delta..psi..sub.j (t) =
(.delta..psi..sub.L(i,j) + .delta..psi..sub.R(i,j))/2 << p/d
POI rotation angle error due to incident angle variation and
condition for image rotation angle control .delta..zeta..sub.j (t)
= (.delta..psi..sub.L(i,j) - .delta..psi..sub.R(i,j))/2 POI tilt
angle error due to incident angle variations .theta..sub.(i,j) =
(.theta..sub.L(i,j) + .theta..sub.R(i,j))/2 image azimuthal angle
.theta..sub.T(i,j) = (.theta..sub.L(i,j) - .theta..sub.R(i,j))/2
image tilt angle .delta..theta..sub.L(i,j) azimuthal angle error of
left beam in POI .delta..theta..sub.R(i,j) azimuthal angle error of
right beam in POI .delta..theta..sub.(i,j) (t) =
(.delta..theta..sub.L(i,j) + .delta..theta..sub.R(i,j))/2 <<
(p/d)tan.theta. condition for controlling image period change due
to azimuthal angle change .delta..theta..sub.T(i,j) (t) =
(.delta..theta..sub.L(i,j) - .delta..theta..sub.R(i,j))/2 <<
(2p/d).sup.1/2 condition for controlling image period change due to
fringe tilts .delta..theta.(t) << 2p/.DELTA.z condition for
controlling image phase change due to fringe tilts and sample z
variation p.sub.(i,j) = .lambda./(2sin.theta..sub.(i,j)) image
period .DELTA..phi..sub.(i,j) = .phi..sub.L(i,j) - .phi..sub.R(i,j)
relative image phase .DELTA.f.sub.(i,j) = f.sub.L(i,j) -
f.sub.R(i,j) = d.DELTA..phi..sub.(i,j) /dt/2.pi. relative image
frequency .chi..sub.(i,j) = .phi..sub.L(i,j) absolute image phase
.xi..sub.(i,j) = .xi..sub.L(i,j) = d.sub..chi.(i,j) /dt/2.pi.
absolute image frequency Q.sub.(i,j) (X,Y) desired spatial
frequency map P.sub.(i,j) (X,Y) = 1/Q.sub.(i,j) (X,Y) desired
period map .THETA..sub.(i,j) (X,Y) = sin.sup.-1
[.lambda./(2P.sub.(i,j))] desired azimuthal angle map A.sub.(i,j)
(X,Y) desired amplitudes map .GAMMA..sub.j (X,Y) = .psi..sub.j -
(.psi..sub.l - .GAMMA..sub.l) desired rotation angles map: CCW
angle between Y axis and fringes .PHI..sub.(i,j) (X,Y) desired
relative phase map .XI..sub.(i,j) (X,Y) desired absolute phase map
G.sub.(i,j) (X,Y) intensity profile of Gaussian beams projected
onto substrate T time duration of exposure ##EQU10## energy dose
absorbed in resist .gamma..sub.K (t) = .psi..sub.j + .GAMMA..sub.j
(X.sub.B,Y.sub.B) locked rotation angle ##EQU11## locked spin
x.sub.K (t) = -X.sub.B cos.gamma..sub.K - Y.sub.B sin.gamma..sub.K
locked x position y.sub.K (t) = X.sub.B sin.gamma..sub.K - Y.sub.B
cos.gamma..sub.K locked y position ##EQU12## locked x velocity
##EQU13## locked y velocity a.sub.K(i,j) (t) = A.sub.(i,j)
(X.sub.B,Y.sub.B) locked amplitude p.sub.K(i,j) (t) = P.sub.(i,j)
(X.sub.B,Y.sub.B) locked period .theta..sub.K(i,j) =
.THETA..sub.(i,j) (X.sub.B,Y.sub.B) locked azimuthal angle
.DELTA..phi..sub.K(i,j) (t) = .PHI..sub.(i,j) (X.sub.B,Y.sub.B)
locked relative image phase .DELTA.f.sub.K(i,j) (t) =
d.PHI..sub.(i,j) /dt/2.pi. = Q.sub.(i,j) (X.sub.B,Y.sub.B)[U.sub.B
(t)cos.GAMMA..sub.j + V.sub.B (t)sin.GAMMA..sub.j ] locked relative
image frequency ##EQU14## locked absolute image phase ##EQU15##
locked absolute image frequency f.sub.0 laser frequency F.sub.(i)
RF frequency .LAMBDA..sub.(i) = S/F.sub.(i) sound wavelength S
sound velocity in AO modulator crystal f.sub.(i) = f.sub.0 +
F.sub.(i) first order Bragg frequency .theta..sub.B(i) =
.lambda.F.sub.(i) /S Bragg angle of first order beam
.theta..sub.(min) minimum angle available .theta..sub.(max) maximum
angle available f.sub.R(i,j) = f.sub.0 + F.sub.R(i,j) first order
Bragg frequency in right arm f.sub.L(i,j) = f.sub.0 + F.sub.L(i,j)
first order Bragg frequency in left arm N.sub..pi. .pi.-phase limit
for phase shifting device V.sub..pi. voltage corresponding to .pi.
phase shift t.sub.FB flyback time f.sub.H = f.sub.0 + F.sub.H
heterodyne frequency of light F.sub.H heterodyne RF frequency
f.sub.LH = f.sub.L - f.sub.H left arm heterodyne frequency f.sub.RH
= f.sub.R - f.sub.H right arm heterodyne frequency .DELTA.f =
f.sub.L - f.sub.R = f.sub.LH - f.sub.RH image frequency (arms
frequency difference) f.sub.ref = f.sub.LH - f.sub.L = F.sub.H
reference heterodyne frequency f.sub.pr = f.sub.LH - f.sub.R =
.DELTA.f + F.sub.H arms phase difference heterodyne frequency
.DELTA.f = f.sub.L - f.sub.R = f.sub.pr - f.sub.ref image frequency
(arms frequency difference) m diffraction order .DELTA..phi..sub.Rm
= -2.pi.m.DELTA.x/p phase shift in right arm due to moving grating
.DELTA..phi..sub.Lm = 2.pi.m.DELTA.x/p phase shift in left arm due
to moving grating .DELTA..phi..sub.m = .DELTA..phi..sub.Lm -
.DELTA..phi..sub.Rm = 4.pi.m.DELTA.x/p image phase shift of due to
moving grating f.sub.R.omega. = -2.pi.m.omega.r/g.sub..omega.
frequency shift in right arm due to spinning grating f.sub.L.omega.
= 2.pi.m.omega.r/g.sub..omega. frequency shift in left arm due to
spinning grating .DELTA.f.sub..omega. = f.sub.L.omega. -
f.sub.R.omega. = 4.pi.m.omega.r/g.sub..omega. frequency shift due
to spinning grating .omega. spin speed of disk beamsplitter grating
r radius of disk beamsplitter grating g.sub..omega. period of
grating on disk beamsplitter .DELTA..phi..sub.D =
(8.pi..DELTA.y/.lambda.)sin.theta.sin.epsilon. phase shift due to
moving substrate .epsilon. angle between y-axis and stage
beamsplitter face x.sub..phi. point defined as zero phase .phi. = 0
x' axis parallel to beamsplitter face y' axis perpendicular to
beamsplitter face .DELTA.f = f.sub.L - f.sub.R image frequency
(phase reference frequency) f.sub.S = .DELTA.f - 2f.sub.D + f.sub.E
stage frequency f.sub.D = (u.sub.S /.lambda.)sin.theta. = u.sub.S
/(2p) Doppler frequency p = u.sub.S /(.DELTA.f - f.sub.S) period
relationship for homodyne case f.sub.E = f.sub.S - .DELTA.f +
2f.sub.D frequency error for homodyne case ##EQU16## phase error
t.sub.0 start time .phi..sub.0 phase at t = t.sub.0 .DELTA.f.sub.H
= .DELTA.f + f.sub.H heterodyne image frequency f.sub.SH =
.DELTA.f.sub.H - 2f.sub.D + f.sub.E heterodyne stage frequency p =
u.sub.S /(.DELTA.f.sub.H - f.sub.SH) period relationship for
heterodyne case f.sub.E = f.sub.SH - .DELTA.f.sub.H + 2f.sub.D
frequency error for heterodyne case f.sub.SLH = f.sub.LH - f.sub.D
+ f.sub.EL left heterodyne stage frequency f.sub.SRH = f.sub.RH -
f.sub.D + f.sub.ER right heterodyne stage frequency f.sub.S =
f.sub.SLH - f.sub.SRH = .DELTA.f - 2f.sub.D + f.sub.E stage
frequency f.sub.EL left arm frequency error f.sub.ER right arm
frequency error f.sub.E = f.sub.EL - f.sub.ER = f.sub.S - .DELTA.f
+ 2f.sub.D frequency error f.sub.DP = (u.sub.S
/.lambda.)(sin.theta. + sin.beta.) Doppler frequency reflected from
stage prism .beta. angle of beam reflected from prism f.sub.SI =
f.sub.DP + f.sub.E measured stage prism Doppler frequency mixed
with incident f.sub.SR = .DELTA.f - 2f.sub.DP + f.sub.E measured
stage prism Doppler frequency mixed with reflected p =
(1/2)/(f.sub.DP /u.sub.S + sin.beta./.lambda.) relationship for
period in prism case f.sub.E = f.sub.SI - f.sub.DP relationship for
frequency error in prism incident case f.sub.E = f.sub.SR -
.DELTA.f + 2f.sub.DP relationship for frequency error in prism
reflected case f.sub.LHD = f.sub.L - f.sub.DP - f.sub.H + f.sub.EL
left hand heterodyne frequency from prism f.sub.RHD = f.sub.R +
f.sub.DP - f.sub.H + f.sub.ER right hand heterodyne frequency from
prism f.sub.E = f.sub.EL - f.sub.ER = .DELTA.f.sub.SR - .DELTA.f +
2f.sub.DP relationship for frequency error in heterodyne prism case
f.sub.Rn = f.sub.R + f.sub.Dn + f.sub.E frequency of nth order
(right) beam diffracted from grating f.sub.Ln = f.sub.L - f.sub.Dn
+ f.sub.E frequency of nth order (left) beam diffracted from
grating f.sub.R2n = f.sub.R + f.sub.Dn + f.sub.ER frequency of nth
order (right) beam diffracted from grating f.sub.L2m = f.sub.L -
f.sub.Dm + f.sub.EL frequency of mth order (left) beam diffracted
from grating f.sub.Dn = nu.sub.S /g nth order Doppler frequency
from grating g grating period f.sub.S1n = f.sub.Dn + f.sub.E stage
frequency from grating (1.sup.st type) f.sub.E = f.sub.Sn1 -
f.sub.Dn relationship for determining frequency error (1.sup.st
type) f.sub.S2n = .DELTA.f - .DELTA.f - f.sub.Dn + f.sub.E
frequency signal from grating(2.sup.nd type) f.sub.E = f.sub.S2n +
f.sub.Dn - .DELTA.f relationship for determining frequency error
(2.sup.nd type) f.sub.S3nm = .DELTA.f - f.sub.Dn - f.sub.Dm +
f.sub.E frequency signal from grating (3.sup.rd type) f.sub.E =
f.sub.EL - f.sub.ER = f.sub.S3nm + f.sub.Dn + f.sub.Dm - .DELTA.f
relationship for determining frequency error (3.sup.rd type)
f.sub.LHGn = f.sub.L - f.sub.Dn - f.sub.H + f.sub.EL left hand
grating Nth order heterodyne frequency f.sub.RHGm = f.sub.R +
f.sub.Dm - f.sub.H + f.sub.ER right hand grating Mth order
heterodyne frequency f.sub.SGmn = f.sub.LHGn - f.sub.RHGm =
.DELTA.f - f.sub.Dn - f.sub.Dm + f.sub.E heterodyne difference
frequency from grating f.sub.E = f.sub.EL - f.sub.ER = f.sub.SGmn +
f.sub.Dn + f.sub.Dm - .DELTA.f relationship for frequency error in
heterodyne grating case
Although the present invention has been shown and described with
respect to several preferred embodiments thereof, various changes,
omissions and additions to the form and detail thereof, may be made
therein, without departing from the spirit and scope of the
invention.
* * * * *